Work and Energy

8.01 W05D1

Next Reading Assignment: W05D2

Young and Freedman: 7.1-7.5,12.3

2

Concept Question: Work and Kinetic Energy

Compared to the amount of energy required to accelerate a car from rest to 10 mph (miles per hour), the amount of work required to accelerate the same car from 10 mph to 20 mph is

(1) the same (2) twice as much (3) three times as much (4) four times as much (5) unsure.

Concept Question: Work and variable force

A particle starts from rest at x = 0 and moves to x = L under the action of a variable force F(x), which is shown in the figure. What is the particle's kinetic energy at x=L/2 and at x=L?

(1) (Fmax)(L/2), (Fmax)(L)

(2) (Fmax)(L/4), 0

(3) (Fmax)(L), 0

(4) (Fmax)(L/4), (Fmax)(L/2)

(5) (Fmax)(L/2), (Fmax)(L/4)

Worked Example: Work Done by the Inverse Square

Gravitational Force Consider a magnetic rail gun that shoots an

object of mass m radially away from the surface of the earth (mass me). When the object leaves the rail gun it is at a distance ri from the center of the earth moving with speed vi . What speed of the object as a function of distance from the center of the earth?

Table Problem: Work Done by Several Forces

A block of mass m slides along a horizontal table with speed v0. At x = 0 it hits a spring with spring constant k and begins to experience a friction force. The coefficient of kinetic friction is given by µ. How far did the spring compress when the block first momentarily comes to rest?

Concept Question: Work and gravity 1

A ball is given an initial horizontal velocity and allowed to fall under the influence of gravity, as shown below. The work done by the force of gravity on the ball is:

(1) positive (2) zero (3) negative

Concept Question: Work and gravity 2

A comet is speeding along a hyperbolic orbit toward the Sun. While the comet is moving away from the Sun, the work done by the Sun on the comet is:

(1) positive (2) zero (3) negative

Table Problem : Asteroid about Sun

An asteroid of mass m is in a non-circular closed orbit about the sun. Initially it is a distance ri from the sun, with speed vi. What is the change in the kinetic energy of the asteroid when it is a distance is rf, from the sun?

Concept Question: Conservation Laws 1

A tetherball of mass m is attached to a post of radius by a string. Initially it is a distance r0 from the center of the post and it is moving tangentially with a speed v0 . The string passes through a hole in the center of the post at the top. The string is gradually shortened by drawing it through the hole. Ignore gravity and any dissipative forces. Until the ball hits the post,

1.  The kinetic energy of the ball is constant.

2.  The kinetic energy of the ball changes.

3.  Not enough information is given to determine whether the kinetic energy of the ball changes or not.

Concept Question: Conservation Laws 2

A tetherball of mass m is attached to a post of radius R by a string. Initially it is a distance r0 from the center of the post and it is moving tangentially with a speed v0. The string wraps around the outside of the post. Ignore gravity and any dissipative forces. Until the ball hits the post,

1.  The kinetic energy of the ball is constant.

2.  The kinetic energy of the ball changes.

3.  Not enough information is given to determine whether the kinetic energy of the ball changes or not.

Demo slide: Spiraling Object

Object spiraling on variable length string as video both with hole and with post.

Concept Question: Trolley

A streetcar is freely coasting around a large circular track. It is then switched to a small circular track. Assume no friction throughout the motion. When coasting on the smaller circle its linear speed is

1. greater 2. less. 3. unchanged.

Pushing a Stalled Car

Concept Question: Pushing against a wall

The work done by the contact force of the wall on the person as the person moves is

1.  positive.

2.  negative.

3.  zero.

4.  impossible to determine from information given in question and the figure.