# Comparing Work Done with Large & Small Masses

• jwxie
In summary: The answer is independent of mass. Work is done regardless of mass. The difference is in the amount of energy used.
jwxie

## Homework Statement

Is more work done on a large or a small mass?

F = d/dt (mv)
W = Fd

## The Attempt at a Solution

Greater the mass, greater the velocity according to F = d/dt (mv)

If the problem is given that
a glider of mass is free to slide along a horizontal air track

one asks this given question, should one consider that, since motion only exists in the x-direction, so the mass is an independent clause? Does this sounds right?

I mean in momentum, when a small mass hits a larger mass, we see the smaller mass moves at a greater velocity, assuming it is elastics.

However, when I look at W = E (mechanical energy) and KE, if the system is conservated with no external force, we always cancel out m (mass).But how come the answer is "no difference"?

jwxie said:
Is more work done on a large or a small mass?

The problem statement is kind of vague. Is it asking

If a constant force is applied to an object over a given distance d, is more work done if the object has large or small mass?

I'm not sure if that's what the question is, but I'll assume it is for now.

F = d/dt (mv)
W = Fd

## The Attempt at a Solution

Greater the mass, greater the velocity according to F = d/dt (mv)

If the problem is given that

one asks this given question, should one consider that, since motion only exists in the x-direction, so the mass is an independent clause? Does this sounds right?

I don't think I follow you. :uhh:

But if you apply a constant force on an object for a set distance d, the work done is independent of the mass. It only depends on the force and distance.

$$W = \vec F \cdot \vec d$$

I mean in momentum, when a small mass hits a larger mass, we see the smaller mass moves at a greater velocity, assuming it is elastics.

However, when I look at W = E (mechanical energy) and KE, if the system is conservated with no external force, we always cancel out m (mass).

But how come the answer is "no difference"?

Perhaps the fact that you are able to "cancel out" m, means that the answer does not depend on m.

If you push a mass, starting from rest, with a constant force F over a distance d, the object will have greater speed when it reaches the distance d if it has a smaller mass. The object would have a slower speed if it has a larger mass. But if you calculate the kinetic energies of the different objects (1/2)mv2, the result is the same for both.

You can convince yourself of this by using the kinematics equations for constant acceleration,

$$d = \frac{1}{2}at^2 +v_0t + d_0$$

$$a = \frac{v_f - v_i}{t}$$

and

$$F= ma$$

Using these equations, calculate the velocity of an object, starting from rest, that has been pushed by a constant force F (on a frictionless surface) for a distance d. Then calculate the object's kinetic energy. You'll find that the kinetic energy is not a function of mass, in this situation. As a matter of fact, you'll find that the kinetic energy is a simple function of force and distance.

jwxie said:

## Homework Statement

Is more work done on a large or a small mass?

... how come the answer is "no difference"?
What's the question?? You are not correctly stating work/energy relationships.

## 1. What is the difference between work done with large and small masses?

The main difference between work done with large and small masses is the amount of force required to move the object. When a large mass is being moved, more force is needed to overcome its inertia, resulting in more work being done compared to a smaller mass. Additionally, the distance over which the force is applied also affects the amount of work done, as more distance means more work is done.

## 2. Is the work done the same if the force and distance are the same for both large and small masses?

No, the work done is not the same for both large and small masses even if the force and distance are the same. This is because the mass of the object is also a factor in determining the amount of work done. A larger mass requires more force to move it the same distance, resulting in more work being done compared to a smaller mass.

## 3. How does the mass of an object affect the amount of work done?

The mass of an object directly affects the amount of work done. As mentioned before, a larger mass requires more force to move it the same distance, resulting in more work being done compared to a smaller mass. This is because of the relationship between force, distance, and work, where work is equal to force multiplied by distance.

## 4. Can a small mass do the same amount of work as a large mass?

No, a small mass cannot do the same amount of work as a large mass. This is because, as discussed before, the amount of work done is dependent on the mass of the object, as well as the force and distance. A small mass has less inertia and requires less force to move it, resulting in less work being done compared to a large mass.

## 5. How does the comparison of work done with large and small masses apply to real-life situations?

The comparison of work done with large and small masses can be seen in various real-life situations, such as lifting heavy objects, pushing a car, or carrying a backpack. In these scenarios, more work is required to move a larger mass compared to a smaller one. This concept is also important in engineering and physics, where the amount of work done is a crucial factor in designing and analyzing systems.

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