# Gravity and Work: Understanding the Relationship between Force and Motion

• rwh
In summary, the question asked about the physics of how gravity acts on a bowling ball, and the answer is that gravity does not act on the bowling ball.
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 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 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?

rwh

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.

rwh said:

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

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.

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.

rwh said:

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!

## 1. How does gravity affect work?

Gravity affects work by exerting a force on objects that are moving in a certain direction. This force, known as weight, is equal to the mass of an object multiplied by the acceleration due to gravity. As objects move against the force of gravity, they are doing work by overcoming this force.

## 2. What is the relationship between gravity and potential energy?

Gravity and potential energy are closely related. Gravity is a conservative force, meaning that it can convert between different forms of energy without any loss. When an object is lifted against the force of gravity, it gains potential energy. This potential energy can then be converted into kinetic energy as the object falls back down.

## 3. How does the strength of gravity affect work?

The strength of gravity affects work by determining the amount of force that needs to be overcome when performing work against it. On Earth, gravity has a constant acceleration of 9.8 m/s², which means that objects will fall towards the ground at the same rate regardless of their mass. However, on other planets or celestial bodies with different gravitational accelerations, the amount of work needed to overcome gravity will be different.

## 4. What is the formula for calculating work against gravity?

The formula for calculating work against gravity is: W = mgh, where W is work (measured in joules), m is mass (measured in kilograms), g is the acceleration due to gravity (measured in m/s²), and h is the height (measured in meters). This formula takes into account the force of gravity and the distance an object is moved against it.

## 5. How is gravity related to the concept of weight?

Gravity is directly related to weight. Weight is a measure of the force of gravity acting on an object. This means that objects with more mass will have a greater weight because they will experience a stronger force of gravity. However, weight can vary depending on the strength of gravity, while mass remains constant regardless of location.

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