p.1
Work and Energy Definitions
What are the two main parts of Chapter 4?
Part 1: Work and Kinetic Energy; Part 2: Potential Energy & Conservation of Energy.
p.9
Work and Energy Definitions
What does it mean to do positive work on an object?
It means you give the object some energy, resulting in a gain of energy for the object.
p.4
Work and Energy Definitions
Why is energy important for society?
It is a big industry and useful for societal functions.
p.44
Conservative vs Non-Conservative Forces
What forces act on the elevator in Example 7.9?
Gravity, a spring (elastic force), and friction.
p.78
Work and Energy Definitions
Which statement is correct regarding the work done by the cable and the elevator?
The cable does positive work on the elevator, and the elevator does negative work on the cable.
p.33
Kinetic Energy and Work-Energy Theorem
How can you find the kinetic energy from an energy diagram?
By analyzing the difference between the total mechanical energy E and the potential energy U(x).
p.17
Conservation of Mechanical Energy
What is the relationship between stored energy and falling objects?
Energy is stored as potential energy and transformed into kinetic energy during the fall.
p.73
Applications of Work and Energy
What is an inclined plane?
A flat surface tilted at an angle to the horizontal.
p.32
Conservation of Mechanical Energy
What is conserved in a spring-mass system when there are no external forces?
The mechanical energy, which is the sum of elastic potential energy and kinetic energy.
p.32
Conservation of Mechanical Energy
What is the relationship between elastic potential energy and kinetic energy in a spring-mass system?
Their sum is a constant value.
p.17
Kinetic Energy and Work-Energy Theorem
What happens to energy as an object falls?
It is transformed from potential energy to kinetic energy.
p.6
Work and Energy Definitions
When does a force do work on an object?
A force does work on an object if the object moves a distance (has a displacement).
p.81
Conservation of Mechanical Energy
What is the relationship between the heights of the two ramps?
The heights y1 and y2 are the same for each ramp.
p.18
Work and Energy Definitions
What is work done in the context of energy transfer?
A transfer of energy that causes a change in energy.
p.5
Work and Energy Definitions
Why do we feel tired when moving heavy objects?
Because we have done work, which requires energy.
p.18
Kinetic Energy and Work-Energy Theorem
How can work done affect kinetic energy?
It can change kinetic energy.
p.7
Work and Energy Definitions
What is the relationship between work done and the components of force?
Work done = F_x * s = F * s * cos(Ο).
p.44
Potential Energy Concepts
What types of potential energies are present in the system described?
Gravitational potential energy and elastic potential energy.
p.33
Work and Energy Definitions
What does an energy diagram represent?
It shows both the potential-energy function U(x) and the total mechanical energy E.
What is the formula for linear momentum?
p = mv (momentum = mass Γ velocity).
p.31
Elastic Potential Energy
What defines an elastic body?
A body is elastic if it returns to its original shape after being deformed.
p.8
Work and Energy Definitions
What determines whether work done by a force is positive, negative, or zero?
The angle between the force and the displacement.
p.2
Newton's Laws of Motion
What does Newton's 1st Law state?
In the absence of external forces, an object at rest remains at rest and an object in motion remains in motion with a constant velocity.
p.34
Work and Energy Definitions
What type of energy is primarily involved in a mass-spring system?
Potential energy and kinetic energy.
p.2
Newton's Laws of Motion
What does Newton's 2nd Law describe?
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
p.6
Work and Energy Definitions
What is the physical meaning of work done?
Work done is a transfer of energy from one object to another.
p.6
Work and Energy Definitions
How does a machine perform work?
A machine does work for you, but you need to supply energy to it (e.g., using electricity or gas).
p.62
Work and Energy Definitions
What formula is used to find the force constant of a spring?
Hooke's Law: F = kx, where F is the force, k is the spring constant, and x is the compression.
p.5
Work and Energy Definitions
What is the relationship between work and energy?
Work is a measure of the energy transferred to or from a system through the action of forces.
p.31
Elastic Potential Energy
What is elastic potential energy?
The energy stored in an elastic body, such as a spring, due to its deformation.
p.26
Conservation of Mechanical Energy
What does the conservation of mechanical energy state?
The sum of kinetic and potential energies remains constant over time.
p.81
Conservation of Mechanical Energy
What principle explains why both blocks have the same speed at the end?
The conservation of mechanical energy states that potential energy is converted to kinetic energy.
p.15
Potential Energy Concepts
What is potential energy?
The energy stored in an object due to its position or configuration.
p.19
Gravitational Potential Energy
What is the formula for gravitational potential energy?
U = mgh, where m is mass, g is gravitational acceleration, and h is height.
p.23
Conservative vs Non-Conservative Forces
What are common examples of non-conservative forces?
Friction and air resistance.
p.42
Applications of Work and Energy
What does the variable 'x' typically represent in physics equations?
It usually represents a position or displacement in space.
p.41
Applications of Work and Energy
What does βπ₯ represent in physics?
The change in position or displacement of an object.
p.44
Work and Energy Definitions
What is the initial energy state of the system?
Initial kinetic energy (KE), initial potential energy (PE), and frictional force.
p.23
Conservative vs Non-Conservative Forces
What can be defined for conservative forces?
Forces associated with potential energy (PE).
p.70
Applications of Work and Energy
What does ππ represent in the context of the glider?
The coefficient of static friction.
What does the conservation of linear momentum state?
Momentum along a certain direction is conserved when there are no external forces acting in that direction.
p.6
Work and Energy Definitions
What is the formula for work done?
Work done (W) = Force (F) Γ Displacement (s).
p.6
Work and Energy Definitions
Can you give an example of work done?
People pushing a car do work on the car.
p.72
Conservation of Mechanical Energy
What does the equation v2^2 = v1^2 - 2khm imply?
The velocity depends on the height of the ball.
p.30
Elastic Potential Energy
How is elastic potential energy increased?
By compressing or stretching a spring.
p.23
Conservative vs Non-Conservative Forces
What is a non-conservative force?
A force where the work done depends on the path taken between initial and final positions.
p.22
Work and Energy Definitions
What must be considered when calculating work done?
Only the displacement parallel to the force.
p.18
Potential Energy Concepts
What is potential energy?
Energy associated with the position or configuration of a mass.
p.65
Newton's Laws of Motion
What role does mass play in motion with a varying force?
The mass of the object affects how much it accelerates in response to the varying force.
p.46
Conservation of Mechanical Energy
What is the equation representing the conservation of mechanical energy?
K1 + U1 + W_total = K2 + U2
p.61
Applications of Work and Energy
What is the significance of Example 6.4?
It illustrates a specific concept or application in the context of the subject matter.
p.44
Conservative vs Non-Conservative Forces
What is the role of friction in the system?
Frictional force opposes the motion of the elevator.
p.25
Conservation of Mechanical Energy
Under what condition is the total mechanical energy of a system conserved?
When only the force of gravity does work on the system.
p.7
Work and Energy Definitions
What component of force does not do any work?
The component perpendicular to the motion.
p.71
Conservation of Mechanical Energy
At the highest point of its trajectory, what is the kinetic energy of a projectile?
It is at its minimum while potential energy is at its maximum.
How is impulse related to momentum?
Impulse is equal to the change in momentum: J = βp.
p.8
Work and Energy Definitions
What is the condition for positive work to be done?
The angle between force and displacement is less than 90 degrees.
p.55
Newton's Laws of Motion
What is drag force in relation to a hammerhead shark?
It is the resistance the shark encounters while swimming through water.
p.30
Elastic Potential Energy
What is the relationship between force and displacement when working on a spring?
Your force and displacement are in the same direction, resulting in positive work.
What is the formula for momentum before and after a collision?
P_initial = P_final, where P_initial = m1 v1 + m2 v2 and P_final = m1 v1' + m2 v2'.
p.21
Gravitational Potential Energy
What occurs when a mass m drops from height m2 to m1?
Work is done by the gravitational force, leading to an increase in kinetic energy.
p.42
Kinetic Energy and Work-Energy Theorem
What does the equation 1 2 mmvΒ² represent?
It represents the kinetic energy of an object, where m is mass and v is velocity.
p.9
Work and Energy Definitions
What happens when you do negative work on an object?
You gain energy from the object, meaning the object loses energy.
p.6
Work and Energy Definitions
What is required to do work?
Energy is needed in doing work.
p.25
Conservation of Mechanical Energy
What is the total mechanical energy of a system?
The sum of its kinetic energy and potential energy.
p.81
Conservation of Mechanical Energy
What is the initial state of the block before it is released?
The block is released from rest.
p.3
Work and Energy Definitions
What is the work done by a force?
The energy transferred to or from an object via the application of force along a displacement.
p.27
Elastic Potential Energy
What is elastic potential energy?
The energy stored in a stretched or compressed spring.
p.24
Conservation of Mechanical Energy
What does the conservation of energy state?
Energy can be transformed from one form to another and from one body to another, but the total amount remains constant.
p.8
Work and Energy Definitions
What happens during positive work?
Energy is transferred by the force to the object.
p.18
Conservation of Mechanical Energy
What happens to work done when lifting an object?
It is converted into potential energy.
p.79
Work and Energy Definitions
After moving 2.00 cm, how does the work done by gravity compare on both blocks?
The work done by gravity is less on the 8.00-kg block than on the 6.00-kg block.
p.2
Newton's Laws of Motion
What is necessary to apply Newton's laws effectively?
Constructing a free body diagram.
p.29
Elastic Potential Energy
What is stored in a stretched or compressed spring?
Energy, referred to as elastic potential energy.
p.14
Work and Energy Definitions
What does the area under the graph of force vs. distance represent?
The work done on the spring to stretch it a distance x.
p.35
Conservation of Mechanical Energy
What is an example of a situation where conservation of mechanical energy is useful?
In a roller coaster, where the forces other than gravitational force can be ignored.
p.80
Newton's Laws of Motion
What happens when a nonzero net force acts on an object?
The object's kinetic energy and velocity cannot both be constant.
p.10
Work and Energy Definitions
What happens to an object's energy when positive work is done?
The object's energy increases.
p.50
Work and Energy Definitions
What is the main focus of Example 6.2?
Finding the total work done by several forces.
p.5
Work and Energy Definitions
How is work defined in physics?
As what is accomplished by a force in moving an object through a distance.
p.44
Elastic Potential Energy
How does elastic potential energy relate to the system?
It is the energy stored in the spring acting on the elevator.
p.82
Conservation of Mechanical Energy
Why is mechanical energy conserved as a rock slides from A to B in a frictionless hemispherical bowl?
Because the normal force acts perpendicular to the bowlβs surface.
What is defined as the impulse of an encounter when a force acts abruptly on an object?
Impulse, J, is defined as J = F βt.
p.71
Kinetic Energy and Work-Energy Theorem
What is the relationship between kinetic energy and speed in projectile motion?
Kinetic energy is proportional to the square of the speed.
p.24
Conservation of Mechanical Energy
What is the definition of mechanical energy?
Mechanical energy is the sum of potential energy and kinetic energy.
p.3
Kinetic Energy and Work-Energy Theorem
What does kinetic energy represent?
The energy that a body possesses due to its motion.
p.21
Potential Energy Concepts
How is the increase in potential energy calculated?
Increase in potential energy = m * g * (m2 - m1).
p.3
Kinetic Energy and Work-Energy Theorem
How does work change the kinetic energy of a body?
Work done on an object results in a change in its kinetic energy, as described by the work-energy theorem.
p.26
Conservation of Mechanical Energy
What does πΎπππ represent?
The total mechanical energy.
p.19
Work and Energy Definitions
What is required to lift an object from a lower height to a higher height?
Work done is needed to increase its potential energy.
p.8
Work and Energy Definitions
What happens during negative work?
Energy is transferred from the moving object.
p.12
Work and Energy Definitions
What does W represent in the work-energy theorem?
The work done by the net force.
p.35
Conservation of Mechanical Energy
How can conservation of mechanical energy be applied to solve problems?
It can be used to find the velocity of a falling object by equating kinetic energy to the change in potential energy.
p.12
Work and Energy Definitions
What is the principle underlying the work-energy theorem?
The principle of conservation of energy.
p.16
Conservative vs Non-Conservative Forces
What are non-conservative forces?
Forces that dissipate mechanical energy, such as friction and air resistance.
p.28
Elastic Potential Energy
What happens to the work done on a spring?
It is stored in the spring as elastic potential energy.
p.41
Applications of Work and Energy
How is βπ₯ calculated?
By subtracting the initial position from the final position (βπ₯ = x_final - x_initial).
p.23
Conservative vs Non-Conservative Forces
What is a conservative force?
A force where the work done depends only on initial and final conditions, not on the path taken.
p.25
Conservation of Mechanical Energy
Give an example of the conservation of mechanical energy.
Motion in a roller coaster.
p.70
Applications of Work and Energy
What is the formula to keep the glider from moving?
ππ π π = πΉπΉ π π πππ‘π‘πππππ.
p.55
Newton's Laws of Motion
What role does gravitational force play for a hammerhead shark?
It pulls the shark downward towards the ocean floor.
p.30
Elastic Potential Energy
What happens when you compress or stretch a spring?
You do work on the spring, increasing its elastic potential energy.
What does Newton's 3rd Law state about the impulse experienced by two colliding bodies?
The impulse experienced by one body is equal in magnitude and opposite in direction to the impulse experienced by the other.
p.16
Potential Energy Concepts
What is potential energy?
The energy stored in an object due to its position or configuration.
p.55
Newton's Laws of Motion
How do these forces interact when a hammerhead shark swims?
The shark must balance buoyant, gravitational, and drag forces to maintain its position and movement.
p.8
Work and Energy Definitions
What is the condition for negative work to be done?
The angle between force and displacement is greater than 90 degrees.
p.24
Conservation of Mechanical Energy
What remains unchanged when an object's gravitational potential energy is added to its kinetic energy?
The total mechanical energy is conserved.
p.19
Work and Energy Definitions
What is the initial velocity of an object when lifted from a lower height?
Initial velocity is zero.
p.15
Potential Energy Concepts
What is an example of potential energy?
A rock held at a height has gravitational potential energy.
p.21
Kinetic Energy and Work-Energy Theorem
Where does kinetic energy come from when a mass falls?
From the change in potential energy.
p.56
Newton's Laws of Motion
What role does gravity play in the use of a hammerhead?
Gravity pulls the hammerhead down, increasing the force of impact when swung.
p.32
Conservative vs Non-Conservative Forces
In a horizontal spring-mass system, which forces are considered to be cancelled?
The gravitational force and the normal force.
p.9
Work and Energy Definitions
What does zero work indicate?
It indicates no energy transfer between you and the object.
p.17
Work and Energy Definitions
How do energy concepts apply to a falling object?
Energy is stored and transformed from one form to another as the object falls.
p.62
Work and Energy Definitions
How do you calculate the total work done on the spring during compression?
Work done (W) = 0.5 * k * x^2, where k is the spring constant and x is the compression.
p.55
Newton's Laws of Motion
What type of forces act on a hammerhead shark?
Buoyant force, gravitational force, and drag force.
p.55
Newton's Laws of Motion
How does buoyant force affect a hammerhead shark?
It helps the shark stay afloat in the water.
p.34
Potential Energy Concepts
What happens to energy in a mass-spring system when it is relaxed?
The system has potential energy stored in the spring.
p.26
Conservation of Mechanical Energy
What is the formula representing the conservation of mechanical energy?
πΎπππ + π1 = πΎ2 + π2.
p.73
Conservative vs Non-Conservative Forces
What role does friction play when moving a crate on an inclined plane?
Friction opposes the motion of the crate, making it harder to move.
p.2
Newton's Laws of Motion
What is the essence of Newton's 3rd Law?
For every action, there is an equal and opposite reaction.
p.29
Elastic Potential Energy
What happens when you relax a stretched or compressed spring?
The spring exerts a force on an object and does positive work on it.
p.30
Elastic Potential Energy
How does inputting energy into the spring affect its elastic potential energy?
It increases the elastic potential energy.
p.16
Elastic Potential Energy
What is elastic potential energy?
The energy stored in elastic materials as the result of their stretching or compressing.
p.12
Work and Energy Definitions
What is the relationship between work and force in the work-energy theorem?
W = F * s, where F is the net force and s is the displacement.
p.56
Newton's Laws of Motion
What is the primary function of a hammerhead?
To deliver force to a nail or similar object.
p.10
Kinetic Energy and Work-Energy Theorem
What happens to the kinetic energy of a ball when a player throws it?
The ball moves faster, resulting in an increase in its kinetic energy.
p.7
Work and Energy Definitions
What is the formula for work done by a constant force acting at an angle?
W = F * s * cos(Ο) or W = F Β· s (dot product of force and displacement vectors).
p.33
Applications of Work and Energy
What is the specific example of an energy diagram mentioned?
The energy diagram for a glider attached to a spring on an air track (with no friction).
p.5
Work and Energy Definitions
What formula represents the work done?
Force x distance = energy spent = work done.
p.31
Elastic Potential Energy
What does X<0 indicate in the context of a spring?
The spring is compressed.
p.15
Conservation of Mechanical Energy
What is the principle of energy conservation?
Energy cannot be created or destroyed, only transformed from one form to another.
p.34
Conservation of Mechanical Energy
What occurs when a mass is displaced from its equilibrium position in a spring?
Potential energy is converted to kinetic energy as it moves.
p.60
Conservative vs Non-Conservative Forces
What does Wf represent in the energy equation?
Work done by non-conservative forces.
p.14
Elastic Potential Energy
What does Hooke's Law state about the force required to stretch a spring?
The force required is proportional to the distance stretched (F = kx).
p.8
Work and Energy Definitions
What is the condition for zero work to be done?
The angle between force and displacement is 90 degrees.
p.16
Elastic Potential Energy
How is elastic potential energy calculated for a spring?
Using the formula PE = 1/2 kxΒ², where k is the spring constant and x is the displacement from the equilibrium position.
p.46
Work and Energy Definitions
What is the work done (W_total) in the given scenario?
W_total = - (17000 N)(2 m) = -34000 J.
p.35
Conservation of Mechanical Energy
In the context of a roller coaster, what can be ignored when considering energy?
The resultant of other forces that are normal to the motion.
p.81
Conservation of Mechanical Energy
What is the condition of the ramps in the problem?
Both ramps are frictionless.
p.72
Conservation of Mechanical Energy
What does the equation 74 KK 1 + U1 = K2 + U2 represent?
It represents the conservation of mechanical energy.
p.72
Kinetic Energy and Work-Energy Theorem
What is the formula for kinetic energy at height h?
1/2 mv1^2 + 0 = 1/2 mv2^2 + mgh.
How is the total linear momentum of a system of two objects calculated?
P = m1v1 + m2v2 = p1 + p2 (vector sum of individual momenta).
p.60
Conservation of Mechanical Energy
What is the principle represented in the equation K1 + U1 + Wf = K2 + U2?
It represents the conservation of mechanical energy.
p.21
Potential Energy Concepts
What happens when you move a mass from m1 to m2?
You do work on it, which is stored as potential energy.
p.70
Applications of Work and Energy
What is the relationship between force and displacement in this scenario?
ππ π π = ππ π₯π₯, where π is the spring constant and π₯ is the displacement.
p.26
Conservation of Mechanical Energy
What are the two components of mechanical energy?
Kinetic energy (K) and potential energy (U).
p.70
Applications of Work and Energy
What values are used to calculate the force needed to keep the glider from moving?
(20 N/m)(0.086 m)(0.1 k)(9.8 m/sΒ²).
p.21
Potential Energy Concepts
What is potential energy?
The energy possessed by a mass due to its height.
p.34
Work and Energy Definitions
What is the relationship between potential energy and kinetic energy in a mass-spring system?
They convert into each other as the mass oscillates.
p.24
Conservation of Mechanical Energy
Under what condition is mechanical energy conserved?
When an object is only influenced by gravitational force, with no other forces acting on it.
p.14
Elastic Potential Energy
What does the variable k represent in Hooke's Law?
k is the force constant (or spring constant) of the spring.
p.60
Applications of Work and Energy
What does the term 'Wn' represent in the energy equations?
Work done by other forces.
p.12
Work and Energy Definitions
What does the term 's' represent in the work-energy theorem?
The displacement of the particle.
p.28
Elastic Potential Energy
Is the work required to compress a spring the same as stretching it?
Yes, the same work is required to compress a spring by x.
p.71
Kinetic Energy and Work-Energy Theorem
What type of energy is primarily involved in projectile motion?
Kinetic energy and potential energy.
p.71
Conservation of Mechanical Energy
What happens to the kinetic energy of a projectile as it rises?
It decreases as potential energy increases.
p.81
Conservation of Mechanical Energy
Which block arrives at the right-hand end with the greater speed?
C. Both blocks arrive at the right-hand end with the same speed.
p.22
Potential Energy Concepts
Does the path of a body affect the expression for gravitational potential energy?
No, it remains the same whether the path is curved or straight.
p.65
Newton's Laws of Motion
How does varying force affect an object's acceleration?
The acceleration of the object changes as the force changes, according to Newton's second law.
p.82
Conservation of Mechanical Energy
What is the role of the normal force in the motion of the rock in the bowl?
It acts perpendicular to the bowlβs surface, allowing for conservation of mechanical energy.
p.65
Newton's Laws of Motion
What is an example of motion with a varying force?
A car accelerating while going uphill, where the force of gravity and engine force vary.
p.29
Elastic Potential Energy
What is the formula for elastic potential energy in a spring?
Elastic potential energy equals 1/2 kxΒ², where k is the spring constant and x is the distance stretched or compressed.
p.27
Elastic Potential Energy
What does the variable 'x' represent in the elastic potential energy formula?
The displacement from the equilibrium position.
p.29
Elastic Potential Energy
How does a spring affect the kinetic energy of an object when relaxed?
The spring increases the kinetic energy of the object by doing positive work.
p.30
Elastic Potential Energy
What is the effect of your work on the elastic potential energy of a spring?
Your work increases the elastic potential energy.
p.22
Work and Energy Definitions
In calculating work done, what type of displacement is used?
Only the displacement parallel to the force.
p.12
Kinetic Energy and Work-Energy Theorem
What is the formula for kinetic energy change in terms of velocity?
ΞK = 1/2 m (v_f^2 - v_i^2)
p.65
Newton's Laws of Motion
What is motion with a varying force?
Motion where the force acting on an object changes over time.
p.71
Conservation of Mechanical Energy
How does energy conservation apply to projectile motion?
The total mechanical energy remains constant if air resistance is negligible.
p.36
Kinetic Energy and Work-Energy Theorem
What is the relationship between kinetic energy and momentum?
K = 1/2 mvΒ² = pΒ² / (2m).
p.19
Kinetic Energy and Work-Energy Theorem
What happens to kinetic energy when an object drops from a height?
Kinetic energy increases due to the change in potential energy.
p.16
Gravitational Potential Energy
How is gravitational potential energy calculated in vertical motion?
It is calculated using the formula PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.
p.60
Applications of Work and Energy
What is the significance of the negative sign in the work done by friction (βf)?
It indicates that friction does work against the motion.
p.73
Work and Energy Definitions
What factors influence the normal force acting on a crate on an inclined plane?
The weight of the crate and the angle of the incline.
p.35
Conservation of Mechanical Energy
What does the kinetic energy of a falling object equal?
The change in potential energy.
p.60
Conservation of Mechanical Energy
What is the total work done from point 1 to point 2?
It is calculated using the energy conservation equation.
p.79
Applications of Work and Energy
What happens to the 8.00-kg block when the 6.00-kg block accelerates downward?
It accelerates to the right.
p.12
Work and Energy Definitions
What does the work-energy theorem state?
The work done by the net force on a particle equals the change in the particleβs kinetic energy over some time interval.
What is the relationship between force, mass, and change in velocity during an impulse?
F = m βv / βt, which can also be expressed as βp / βt.
p.22
Potential Energy Concepts
What does the potential energy difference between two points depend on?
The difference in vertical distance between the two points (y2 - y1).
p.21
Work and Energy Definitions
How is work done related to kinetic energy?
Work done = m * g * (m2 - m1) = increase in kinetic energy.
p.2
Newton's Laws of Motion
What is the resultant force?
The vector sum of all the forces on an object.
p.16
Conservation of Mechanical Energy
What does the conservation of mechanical energy state?
In a closed system, the total mechanical energy remains constant if only conservative forces are acting.
How does the mass of a hammerhead affect its performance?
A heavier hammerhead can deliver more force upon impact due to greater momentum.
p.22
Potential Energy Concepts
What type of distance is necessary in the expression of potential energy?
Only vertical distance, because the force is vertical.
p.24
Conservation of Mechanical Energy
What happens to an object's kinetic energy when it falls from a height?
The object's kinetic energy increases, equal to the decrease in its gravitational potential energy.
p.3
Relating work and kinetic energy
How are work and kinetic energy related?
Work is equal to the change in kinetic energy of an object.
p.27
Elastic Potential Energy
What is the relationship between force and displacement in a spring?
F = -kx, where F is the force applied, k is the spring constant, and x is the displacement.
p.46
Kinetic Energy and Work-Energy Theorem
What does K1 represent in the conservation of energy equation?
The initial kinetic energy, calculated as 1/2 mv1^2.
p.29
Elastic Potential Energy
What happens to elastic potential energy when the spring is relaxed?
It is converted into kinetic energy of the object.
p.56
Newton's Laws of Motion
What forces act on a hammerhead when it is swung?
Gravity, applied force from the swing, and resistance from the object being struck.
p.56
Conservative vs Non-Conservative Forces
What is the effect of resistance on a hammerhead's motion?
Resistance from the object being struck can reduce the hammerhead's speed and force upon impact.
p.39
Elastic Potential Energy
What is the velocity of the glider at Position 2?
To be determined (requires calculation).
p.15
Gravitational Potential Energy
How is gravitational potential energy calculated?
Gravitational potential energy is calculated using the formula PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.
p.73
Work and Energy Definitions
How does the angle of the incline affect the force required to move the crate?
A steeper incline increases the gravitational component acting down the slope, requiring more force to move the crate.
p.15
Work and Energy Definitions
What role does potential energy play in mechanical systems?
Potential energy can be converted into kinetic energy, influencing the motion of objects.
p.2
Newton's Laws of Motion
How can the resultant force be obtained?
By considering the component sum of all forces.
p.28
Elastic Potential Energy
What is the relationship between force and distance when stretching a spring?
The force required to stretch a spring a distance x is proportional to x: F = kx.
p.20
Gravitational Potential Energy
What is the formula for work done in terms of gravitational potential energy?
W_ext = -F_G (m2 - m1) = -m * k * m
p.16
Gravitational Potential Energy
What is gravitational potential energy?
The potential energy associated with an object's height above the ground.
p.18
Work and Energy Definitions
What does lifting an object involve in terms of energy?
Doing work that increases the object's potential energy.
p.20
Gravitational Potential Energy
What does the work done when an object is dropped from m2 to m1 equal?
W_ext = (U_g)2 - U_g1 = βU_g = m * k * (m2 - m1)
p.22
Potential Energy Concepts
What is the formula for potential energy?
P.E. = mgh (where m is mass, g is gravitational acceleration, and h is height).
p.8
Work and Energy Definitions
What occurs during zero work?
No energy is transferred to or from the moving object.
p.35
Conservation of Mechanical Energy
Why is using conservation of mechanical energy convenient in some scenarios?
It avoids the need to use force, especially when the force is not constant.
p.28
Elastic Potential Energy
What does the variable k represent in the spring force equation?
k is the force constant (or spring constant) of the spring.
p.73
Work and Energy Definitions
What is the formula for calculating the force of friction on an inclined plane?
Friction force = coefficient of friction Γ normal force.
p.20
Gravitational Potential Energy
What is the relationship between work done and change in gravitational potential energy?
The work done is equal to the change in gravitational potential energy.
p.16
Conservative vs Non-Conservative Forces
What are conservative forces?
Forces that do not dissipate mechanical energy, such as gravity and spring force.
p.20
Gravitational Potential Energy
What does the negative sign in the work done formula indicate?
It indicates that work is done against the gravitational force.
p.46
Kinetic Energy and Work-Energy Theorem
How is the initial kinetic energy (K1) calculated for a mass of 2000 kg moving at 4 m/s?
K1 = 1/2 (2000 kg)(4 m/s)^2 = 16000 J.
p.28
Work and Energy Definitions
What does the area under the force vs. distance graph represent?
The work done on the spring to stretch it a distance x.
