Work & Energy Notes

What is work?When we use it every day, we say we do work when we have to put in effort to accomplish something.

In physics it means the same thing – putting in effort to accomplish something. But we need to define what we mean by effort and accomplishing something.

Putting in effort means exerting a force on an object.

Accomplishing something means making the object move – it has to go some distance.

To do physical work means to exert a force that

makes an object move.

We put both of those measures into mathematical form so we can calculate

how much work you do.

W = F · dW = Work F = Force d = distance

Together, do this problem from the class exercises. Look at units.

1. You have to pull with 125 N to the east to drag a dead tree branch 20 m to the east across your yard. How much work do you do on the tree branch?

Do this problem individually. Ask for help from teacher or peers if you need it.

2. You catch a ball moving toward you by pushing with 280 N against the motion while your hand moves 0.4 m with the ball. How much work do you do?

Now consider the situation shown in this clip:

(Click on this text to activate hyperlink)

Does the man do any work on the bricks as he carries them across the level plank?

No! The man does not do any work

on the bricks while carrying them across the level plank.

He is exerting a force on the bricks – pushing them up to fight gravity.

Why not?

And he is moving a distance to the right across the plank.

But the force and the motion are not connected. An upward force cannot cause something to move to the right. It can only be involved in upward or downward motion

In order for work to be done, the force and the

distance must be going in the same direction!

What if the force and motion aren’t in the same direction?

Find the component of the force in the direction of the motion and plug that into

the Work formula.

Do problem 4 individually.

Together, do this problem from the class exercises. Look at units.

3. A search and rescue team hauls an injured skier on a sled along a flat, 2000 m section of ground. The rescuers drag the skier by pulling on a rope with 500 N at 30° above horizontal. How much work do the rescuers do?

4. Jake pushes his dog 1.5 m to get it out of the way of the door by shoving with a force of 160 N at 40° below horizontal. How much work does he do on the dog?

Do this problem individually. Ask for help from teacher or peers if you need it.

What happens to an object when you do work on it?

It depends. There are lots of possibilities.

We’ll look at a couple today.

Why do we care about work? Why is work an important concept?

The first possibility is if the force doing the work is an unbalanced (or net) force.

In that case, the object will accelerate (according to Newton’s Second Law). We rework the equation to use the idea of work:

Fnet = ma

Fnet·d = m(a·d) But vf2 = vi

2 + 2a·d

So, a·d = ½vf2 – ½vi

2

Fnet·d = m(½vf2 – ½vi

2)

Fnet·d = ½mvf2 – ½mvi

2

This equation is another way of saying Newton’s second law – that an unbalance force makes an object accelerate. To understand it, we need to define those funny terms on the right.

What is ½mv2 ?

We call it Kinetic Energy!K = ½mv2

Kinetic Energy is a lot like momentum – it is another way to talk about a moving object.

Kinetic Energy is also like momentum in that you get it by multiplying mass and velocity. But the details are different!

5. How much kinetic energy does an 8 kg bowling ball traveling at 10 m/s have? How much momentum does it have?

Together, do this problem from the class exercises. Look at units.

Do this problem individually. Ask for help from teacher or peers if you need it.

6. How much kinetic energy does a 4 kg bowling ball traveling at 20 m/s have? How much momentum does it have?

Now we can complete our rewrite of Newton’s 2nd Law : Fnet·d = ½mvf

2 – ½mvi2

Wnet = Kf – Ki

Fnet·d = Wnet ½mvf2 = Kf ½mvi

2 = Ki

First:

Doing work on an object with an unbalanced force changes the object’s

kinetic energy.

This is just another way to say that the object accelerates when a force acts on it (Newton’s 2nd Law), but it turns out to be a useful

way.

You can read this equation two ways (meaning it tells you two different things).

Second:

When an object loses kinetic energy, it does work against what ever it hits.

And that is the best definition for what it means to have energy.

Energy is the ability to do work.

7. When you hit a 0.045 kg golf ball with a driver, the ball speeds up from rest to 70 m/s while the club pushes it for 1.5 cm (that’s how far the ball moves while the club is in contact with the ball).

a) How much kinetic energy does the ball have when it is at rest?

 

b) How much kinetic energy does the ball have when it is moving at 70 m/s?

 

c) How much work does the club have to do to speed the ball from rest to 70 m/s?

 

d) How much force does the club exert on the ball while they are in contact?

Together, do this problem from the class exercises. Look at units.

8. A hockey player skates up behind a 0.227 kg puck traveling 5 m/s along the ice and flicks it so that it speeds up to 30 m/s.

a) How much kinetic energy does the puck have when it is traveling 5 m/s?

 

b) How much kinetic energy does the puck have when it is traveling 30 m/s?

 

c) How much work does the stick have to do to speed the puck from 5 m/s to 30 m/s?

 

d) If the stick exerts 5000 N of force on the puck, how far does the puck move while the stick is in contact with it?

Do this problem individually. Ask for help from teacher or peers if you need it.

9. When you fire a rifle, the 0.016 kg bullet speeds up from 0 m/s to 300 m/s as it travels down the barrel of the rifle. The bullet experiences 1000 N of friction as it slides down the barrel. If the barrel of the rifle is 0.8 m long, how much force does the gun have to exert on the bullet?

Together, do this problem from the class exercises. Look at units.

10. You drive your 1200 kg car onto the highway on-ramp going 10 m/s and hit the gas to get up to 30 m/s so you can merge with the freeway traffic. There is 1500 N of friction against your car’s motion. If your engine can exert 5000 N of force, how long should the on-ramp be so that you can get up to 30 m/s by the time you reach the end?

Do this problem individually. Ask for help from teacher or peers if you need it.

11. You hit the brakes and 11000 N of friction slows your 1000 kg car down from 30 m/s to rest. How far does your car move while it is coming to a stop?

Together, do this problem from the class exercises. Look at units.

12. You hit the brakes and 11000 N of friction slows your 1000 kg car down from 45 m/s to rest. How far does your car move while it is coming to a stop?

Do this problem individually. Ask for help from teacher or peers if you need it.

Objects can have the ability to do work because they are in motion – they can have kinetic energy.

Objects can also get the ability to do work in other ways.

For example, when you pick something up you do work pushing it up against gravity. Your work does not go into giving the object kinetic energy (except a little bit at the very beginning), it goes into fighting gravity.

But once you pick something up and have it sitting up in the air, it is now capable of doing work when it falls.

Gravity pulling down on it gives it the ability to do work – Gravity gives it energy

We call the energy you get from a force pulling on potential energy – in this case we call it gravitational potential energy

Do this problem individually. Ask for help from teacher or peers if you need it.

Together, do this problem from the class exercises. Look at units.

13. You have a 5 kg bowling ball.a) How much gravitational potential energy does it have sitting on the rack 50 cm off the floor?

13. You have a 5 kg bowling ball.b) How much gravitational potential energy will it have when sitting on a shelf 2 m above the floor

Together, do this problem from the class exercises. Look at units.

14. After a track meet, the athletes have to push a 20 kg cart loaded with 80 kg of equipment up the hill to the gym. The hill is 100 m long and angled at 10° above horizontal. The wheels are essentially frictionless.

a) How much gravitational potential energy does the loaded cart have at the bottom of the hill?

b) How much gravitational potential energy does the loaded cart have at the top of the hill?

 

c) How much work do the athletes have to do to push the cart up the hill?

Do this problem individually. Ask for help from teacher or peers if you need it.

15. Michaela lifts a 50 kg box from a table that is 0.9 m off the ground up onto a shelf that is 2.3 m off the ground.a) How much gravitational potential energy does the box have on the table? 

b) How much gravitational potential energy does the box have on the shelf?  

c) How much work does Michaela do lifting the box?