Gravity and Work: Understanding the Relationship between Force and Motion

[rwh]

I have a question that is probably pretty basic. On a test my teacher gave he asked the following question:

Why does the force of gravity do no work on a bowling ball rolling along a bowling alley?

I answered:

I disagree with this statement. The bowling ball has mass so gravity is acting on the bowling ball proportionally to its mass. Just because the bowling ball is on a slippery surface where there is little friction does not mean that the law of universal gravitation does not apply. So gravity is working on the bowling ball while it is rolling along the bowling alley.

The correct answer was:

the direction of the force of gravity is perpendicular to the motion no work

This is an online class and I copied every thing directly. Where is my reasoning wrong? And what principles did I forget?

Thanks for your help,
rwh

 

[mrjeffy321]

well the definition of work is
W = force [in the direction of movement] * displacement.

if gravity is acting straight down and the bolwing ball is moving perfectly horizontally, then to get the force in the direction of movement,
F*cos(90) = 0, so there is no force being aplied in the direction of movement.

this is similar to the fact that if you are holding a heavy weight in your arms, and the weight is not being lifted or lowered, then no work is being done on it, although the person holding it may argue differently, since there is no movement/displacement, no work.

 

[Andrew Mason]

The correct answer was:

the direction of the force of gravity is perpendicular to the motion no work

This is an online class and I copied every thing directly. Where is my reasoning wrong? And what principles did I forget?

If work is done to the ball, it would gain energy (ie it would speed up or gain potential energy).
Work is defined as:

$$W = \int \vec F \cdot d\vec{s}= \int cos\theta mgds$$

where $\theta$ is the angle between the gravitational force and the direction of the object's motion. If that angle is 90 deg, cos 90 = 0 so the work done is 0.

If the floor is sloped, the work done by gravity would be non-zero. But most bowling alleys are pretty flat.

AM

 

[whozum]

Basically, as the ball is rollign down the alley, gravity is not playing any part in the ball's energy state (relative to the ground). Therefore gravity does no work.

 

[Werg22]

Because it has no component in the direction of the ball... hey perpendicular to each other and thus independant. But on the other hand the weight gravity applies on the alley causes friction.

 

[Doc Al]

I answered:

I disagree with this statement. The bowling ball has mass so gravity is acting on the bowling ball proportionally to its mass. Just because the bowling ball is on a slippery surface where there is little friction does not mean that the law of universal gravitation does not apply. So gravity is working on the bowling ball while it is rolling along the bowling alley.

I think part of the confusion is that you understood the question as asking "why doesn't gravity act on the bowling ball". And, given that interpretation, you answered correctly that of course gravity acts on the bowling bowl. But the question was about the work done by the force of gravity, which has a specific meaning in physics. As others have explained, the work done by the gravitational force is zero in this case.

So, in a sense, gravity certainly "works" on the bowling ball (it pulls the ball downward), but it does no work (in the physics sense) on the ball. Everyday words often have precise technical meanings in physics. Beware!