Group Work

1. A perfectly elastic ball of mass m collides with velocity v directly perpendicular into a rigid, massive wall. a. What is the direction of the net force on

the ball as it squishes into the wall?

b. What is the direction of the net force on the ball as it pushes away from the wall?

v

Group Work

1. A perfectly elastic ball of mass m collides with velocity v directly perpendicular into a rigid, massive wall.

c. What is the sign of the work done on the ball as it squishes into the wall?

d. What is the sign of the work done on the ball as it pushes away from the wall?

Group Work

1. A perfectly elastic ball of mass m collides with velocity v directly perpendicular into a rigid, massive wall.

e. If the ball’s initial and final speeds are equal, what is the net work done on the ball?

Announcements

• Exam 2 Thursday– impulse, momentum, Newton’s third law,

conservation of momentum, work, kinetic energy, gravitational potential energy

– Standards 6–9

• First re-do of Standards 2–5 Thursday too– If you do the practice problems before Wed

Work-Energy Theorem

• The work done on an object by the net force acting on it is its change in kinetic energy.

∑F·r = K

Objective

• Calculate the average power necessary to change an object’s energy by a given amount in a given time.

Power

Rate of doing work

E = change in energy ( = work)

t = time interval

Power =E

t=

w

t

Units of Power

= J/s = W = watt

Power =E

t

W =kg m2

s2 s

kg m2

s3=

Energytime

Group Work

2. The 2004 Tour de France’s Alpe d’Huez time trial stage was a steep climb with its finish 1200 m higher than the start. Lance Armstrong won with a time t of 39:41 (2381 s). He and his gear had a combined mass of 84 kg.

 

What was Lance’s average power E/t during the stage?

Hint: Use change in gravitational potential energy for E.

Power

A different but equivalent formula

Power =w

t=

F·d

t= F·v

v = velocity

d = change in position

Example Problem

Show that (force·velocity) gives the same units as (work/time).

force units =

velocity units =

work units =

time units =

Conservation of Energy

What’s the point?

• Nature keeps careful account of energy.

Objectives

• Track energy transfers in interactions.

Which is greater?

A. The force F1 exerted downward on the lever arm

B. The force F2 exerted upward on the rock

C. They are the same magnitude

Think Question

Which is greater?

A. The distance d1 traveled by the lever arm

B. The distance d2 traveled by the rock

C. They are the same distance

Think Question

Which is greater?

A. The work done on the lever arm

B. The work done on the rock

C. They are the same

Poll Question

Simple Machines

• Input and output forces can be different

• Trade-off is distance traveled

• Work is unchanged– work input = work output

Simple Machines

Conservation of Energy

• Energy can be transferred between objects or transformed into different forms, but the total amount of energy can never change.

Convert Potential Kinetic

Gravity exerts force mg as object drops distance h.

work = mgh

PE decreases mgh

KE increases mghSource: Griffith, The Physics of Everyday Phenomena

Conservation of Energy

Source: Griffith, The Physics of Everyday Phenomena

Think Question

The piglet has a choice of three frictionless slides to descend. Which slide’s path gives the piglet the greatest change in potential energy?

A B C

D. Same for all.

Think Question

The piglet has a choice of three frictionless slides to descend. At the end of which slide will the piglet have the greatest kinetic energy?

A B C

D. Same for all.

Poll Question

The piglet has a choice of three frictionless slides to descend. Down which slide will the piglet have the greatest speed at the end?

A B C

D. Same for all.

Poll Question

If the slides have friction, with the same against the piglet, along which is the force of friction the greatest?

A B C

D. Same for all.

Poll Question

If the slides all have the same > 0 against the piglet, along which will friction do the most (negative) work on the piglet?

A B C

D. Same for all.

Poll Question

All three slides have the same > 0 against the piglet. Down which slide will the piglet have the greatest speed at the end?

A B C

D. Same for all.

Rebound and Stop

initial v final v

initial v final v = 0

Think Question

Which changes its momentum the most?

A. A moving object that stops when it hits a barrier.

B. A moving object that bounces back from a barrier.

Hint: Momentum is a vector.

Poll Question

Which changes its kinetic energy the most?

A. A moving object that stops when it hits a barrier.

B. A moving object that bounces back from a barrier.

Hint: kinetic energy depends on speed, not direction.

Inelastic Collisions

• Total kinetic energy decreases.

• Work done against friction and drag:– is not stored as potential energy– cannot be recovered as kinetic energy

• Thermal energy increases.• Energy is conserved!

Reading for Next Time

• Uniform circular motion

• Big ideas:– Direction of motion changes but speed does

not.– Acceleration and net force are well-defined,

with a specific direction.