Kinetic and Potential EnergyKinetic and Potential Energy

PhysicsPhysics

Ms. LiMs. Li

Kinetic EnergyKinetic Energy

The energy of motionThe energy of motion

The net work done on an object is equal to The net work done on an object is equal to the the change change in kinetic energy of an object.in kinetic energy of an object.

Work = Work = ΔΔKEKE

Fd = mad= m(1/2(vf^2-vi^2)=1/2mvf^2-Fd = mad= m(1/2(vf^2-vi^2)=1/2mvf^2-1/2mvi^2= KEf - KEi1/2mvi^2= KEf - KEi

Kinetic EnergyKinetic Energy

KE = ½mvKE = ½mv22

This equation reveals that the kinetic energy of an object is directly

proportional to the square of its speed. That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. For a

threefold increase in speed, the kinetic energy will increase by a factor

of nine.

Energy is scalar

Kinetic energy is a scalar quantity; it does not have a direction. Unlike velocity, acceleration, force, and momentum, the kinetic energy of an object is completely described by magnitude alone.

Check Your Understanding

1. Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.

2. If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy?

Check Your Understanding

1. KE = 0.5*m*v2 KE = (0.5) * (625 kg) * (18.3 m/s)2KE = 1.05 x105 Joules 2. If the speed is doubled, then the KE is quadrupled. Thus, KE = 4 * (1.04653 x 105 J) = 4.19 x 105 Joules. orKE = 0.5*m*v2KE = 0.5*625 kg*(36.6 m/s)2KE = 4.19 x 105 Joules

Examples

3.Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 12 000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed?4. A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic energy if it is moving at 30 mi/hr.

Answers 3.KE = 0.5*m*v2 12 000 J = (0.5) * (40 kg) * v2

300 J = (0.5) * v2

600 J = v2

v = 24.5 m/s

4. KE = 80 000 J

 The KE is directly related to the square of the speed. If the speed is reduced by a factor of 2 (as in from 60 mi/hr to 30 mi/hr) then the KE will be reduced by a factor of 4. Thus, the new KE is (320 000 J)/4 or 80 000 J.

ExampleExample

How much work is required to accelerate a How much work is required to accelerate a 1000 kg car from 20 m/s to 30 m/s?1000 kg car from 20 m/s to 30 m/s?

ExampleExample5.A car traveling 60 km/hr can brake to a stop 5.A car traveling 60 km/hr can brake to a stop within a distance of 20 m. If the car is going within a distance of 20 m. If the car is going twice as fast, 120 km/h, what is its stopping twice as fast, 120 km/h, what is its stopping distance?distance?

What is Potential Energy?What is Potential Energy?

Stored energy.Stored energy.

Can be used later to do workCan be used later to do work

Depends on:Depends on:– Position of object (ex. Height)Position of object (ex. Height)– Configuration of object(ex. Stretched spring)Configuration of object(ex. Stretched spring)

Examples of PE.Examples of PE.

Wound up clock spring.Wound up clock spring.

A book about to fall off a tableA book about to fall off a table

GasolineGasoline

FuelFuel

Gravitational PEGravitational PE

Depends on heightDepends on height

Depends on massDepends on mass

Depends on Depends on acceleration due to acceleration due to gravitygravity

PEPEgravgrav= mgh= mgh

Work and PEWork and PE

When work is done When work is done on an object often the on an object often the PE of an object PE of an object changes.changes.

If an object is lifted If an object is lifted upward the PEupward the PEgrav grav

increasesincreases

Hmm… that guy has a lot of PE!

Knowing that the potential energy at the top of the tall platform is 50 J, what is the potential

energy at the other positions shown on the stair steps and the incline?

Elastic PEElastic PE

Often when a spring is compressed it Often when a spring is compressed it gains potential energy.gains potential energy.

The formula for the force of a spring isThe formula for the force of a spring isF = -kxF = -kx

F = force(N)F = force(N)

k = spring constant(N/m)k = spring constant(N/m)

x = displacement of spring (m)x = displacement of spring (m)

Elastic PEElastic PE

When a spring is stretched or compressed When a spring is stretched or compressed there must be work done on the spring.there must be work done on the spring.

This work done gives the spring PEThis work done gives the spring PE

Equation:Equation:PEPEelasticelastic= ½kx= ½kx22

ExampleExample

A 1000 kg roller A 1000 kg roller coaster moves from coaster moves from point A to point B and point A to point B and then to point c. What then to point c. What is the change in PE is the change in PE as the car moves as the car moves form B to C?form B to C?

A

B

C

15 m

10m

Mechanical EnergyMechanical Energy

The total amount of potential and kinetic The total amount of potential and kinetic energy an object has.energy an object has.

If all the forces acting on an object are If all the forces acting on an object are conservative then the total mechanical conservative then the total mechanical energy of the system can be given as:energy of the system can be given as:

E = KE + PE + QE = KE + PE + Q

E = ½mvE = ½mv22 + PE +Q + PE +Q

Conservation of EnergyConservation of Energy

The total mechanical energy of a system The total mechanical energy of a system neither increases nor decreases in any neither increases nor decreases in any process. It stays constant. This is true process. It stays constant. This is true only if only conservative forces are acting only if only conservative forces are acting in the system.in the system.

In other words : If an object falls all of its In other words : If an object falls all of its potential energy turns into kinetic energy potential energy turns into kinetic energy by the time it reaches zero height.by the time it reaches zero height.

Problem solvingProblem solving

Remember that an objects PE changes Remember that an objects PE changes into KE as it loses height.into KE as it loses height.

For example, a ball rolls down a For example, a ball rolls down a frictionless incline plane of height H. It frictionless incline plane of height H. It then rolls up another frictionless incline then rolls up another frictionless incline plane of height 2H.plane of height 2H.

The height that the ball reaches must be The height that the ball reaches must be only halfway up the second ramp. (H)only halfway up the second ramp. (H)

ExamplesExamples

Estimate the kinetic energy and the Estimate the kinetic energy and the velocity required for a 70 kg pole vaulter velocity required for a 70 kg pole vaulter to pass over a bar 5.0 m high. Assume to pass over a bar 5.0 m high. Assume the pole vaulter’s center of mass is the pole vaulter’s center of mass is initially 0.90 m off the ground and initially 0.90 m off the ground and reaches its maximum height at the level reaches its maximum height at the level of the bar itself.of the bar itself.

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