A red ball has a mass of 250 g. A constant force pushes the red ball horizontally and launches it at a speed of 15 m/s . The same force pushes a green ball through the same distance, launching it at 25 m/s. What is the mass of the green ball?

Question

Accepted Answer

Hey, everyone. So this problem is dealing with the work energy theorem. Let's see what they're asking us. They're asking us how much work is required to accelerate a block of a given mass from rest to 15 m per second if a given force is applied in the direction of motion. So because the block starts at rest, we can recall that through the work energy theorem, that means that the work is equal to the change in kinetic energy, or we'll say work is equal to delta K. We can also recall that Kr kinetic energy is given as one half M V squared. So delta K is just K F minus K initial. So one half M, the F squared minus one half M, the ise squared. And we know that we start from rest. So our initial speed is zero. So the entire time just goes to zero. And from there, we are given the last two things that we need. We know that the mass is 250 g. It's going to put that in standard units. I'm gonna rewrite that as .25 kg and our speed Is 15 m/s. So our work is equal to our delta K. So work is equal to one half times the mass Times the final speed squared. And when we plug that in to our calculators, we get 28.1 jules. And so that is the answer to this problem. We look at our potential answers and that aligns with choice. See, and so that's what we've got for this one. That's all we'll see you in the next video.

A red ball has a mass of 250 g. A constant force pushes the red ball horizontally and launches it at a speed of 15 m/s . The same force pushes a green ball through the same distance, launching it at 25 m/s. What is the mass of the green ball?

Verified Solution

Key Concepts

Newton's Second Law of Motion

Kinetic Energy

Conservation of Energy