Work and Energy (Concept Test)

6.1 To Work or Not to Work
Is it possible to do work on an object that remains at rest?

• yes

• no

Answer explanation

Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done.

6.2a Friction and Work I
A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

• friction does no work at all

• friction does negative work

• friction does positive work

Answer explanation

Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work: W = Fdcosθ since θ = 180^o, then W < 0.

6.2b Friction and Work II
Can friction ever do positive work?

• yes

• no

Answer explanation

Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of friction that is making the box move.

6.2c Play Ball!
In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball?

• catcher has done positive work

• catcher has done negative work

• catcher has done zero work

Answer explanation

The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = Fdcosθ), since θ = 180^o, then W < 0. Note that because the work done on the ball is negative, its speed decreases.

6.2d Tension and Work
A ball tied to a string is being whirled around in a circle.  What can you say about the work done by tension?

• tension does no work at all

• tension does negative work

• tension does positive work

Answer explanation

No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work: W = Fdcosθ since θ = 90^o, then W = 0.

6.3 Force and Work
A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

• one force

• two forces

• three forces

• four forces

• no forces are doing work

Answer explanation

A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

6.4 Lifting a Book
You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book?

• mg x Δr

• F_HAND x Δr

• (F_HAND + mg) x Δr

• zero

• none of the above

Answer explanation

The total work is zero since the net force acting on the book is zero. The work done by the hand is positive, while the work done by gravity is negative. The sum of the two is zero. Note that the kinetic energy of the book does not change, either!

6.5a Kinetic Energy I
By what factor does the kinetic energy of a car change when its speed is tripled?

• no change at all

• factor of 3

• factor of 6

• factor of 9

• factor of 12

Answer explanation

Since the kinetic energy is ½mv², if the speed increases by a factor of 3, then the KE will increase by a factor of 9.

6.5b Kinetic Energy II
Car #1 has twice the mass of Car #2, but they both have the same kinetic energy. How do their speeds compare?

• 2v₁ = v₂

• √2v₁ = v₂

• 4v₁ = v₂

• v₁ = v₂

• 8v₁ = v₂

Answer explanation

Since the kinetic energy is ½mv², and the mass of Car #1 is greater, then Car #2 must be moving faster. If the ratio of m₁/m₂ is 2, then the ratio of v² values must also be 2. This means that the ratio of v₂/v₁ must be √2.

6.6a Free Fall I
Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one?

• quarter as much

• half as much

• the same

• twice as much

• four times as much

Answer explanation

Consider the work done by gravity to make the stone fall distance d:

ΔKE = W_net = F d cosθ

ΔKE = mg d

Thus, the stone with the greater mass has the greater KE, which is twice as big for the heavy stone.