A softball having a mass of 0.25 kg is pitched horizontally at...

Question

A softball having a mass of 0.25 kg is pitched horizontally at 120 km/h. By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distance between the plate and the pitcher is about 15 m.

Accepted Answer

Welcome back. Everyone in this problem. A 0.016 kg rubber bullet was fired horizontally at a shooting target 18 m away. After the bullet left the barrel, it had an initial speed of 216 kilometers per hour. Upon reaching the target, its speed dropped by 15%. Ignoring gravity, calculate the average jug force due to air on the bullet for our answer traces A says it's 0.44 newtons, B 1.6 newtons, C 5.8 newtons and D 21 newtons. Now let's try to visualize what's really going on here. So we're talking about a bullet, ok? That was fired at a shooting target 18 m away. So let's say that this is our shooting target, ok? And let's call that distance that it traveled 18 m. Let's call that distance D OK. Now we know and this is our bullet, ok? We know, ok. That initially our bullet had a speed of 216 kilometers per hour. So let's call that V one. But now upon reaching the target, its speed dropped by 15%. So now V two, we can call that second speed V two, which is 15% less than V one. In other words, 85% of V one or 0.85 V one, ok? And we are trying to calculate the average drug force due to air on the bullet. Now, if we think about it, if our bullet is going in this direction, then our jug force would be going opposite. In other words, it would be going towards the left and we want to find the drug force which in this case, we can call FF. So that's what we're trying to figure out. So now we're talking about forces and we're thinking about distance and speeds. What do we know that relates force and distance? Well, we can recall, OK, that the work done is equal to the force multiplied by the distance traveled multiplied by the cosine of theta. OK? That is the angle between uh the angle that is formed here between the jug force, the force and the displacement rather. So in this case, since we're talking about the work done due to the drug force, we can call that WF So that means WF equals the force due to the average drug force FF multiplied by D multiplied by the cosine of theta. Now, since they're going in the opposite direction, that means the angle between them is 180 degrees, not a cosine of 180 degrees equals negative one. So therefore, that tells us FD, equal, sorry, negative FD, negative one multiplied by FD equals the work done. So therefore, our force, OK is going to be equal to negative W divided by D. Now we know what our distance is, but we don't know the work that was done. That's, that's where our problem lies. OK? So if we can figure out the work that was done, then we will be able to figure out the average drug force due to air. Let's think about all the information we have so far. So so far, we know that our initial speed was 216 kilometers per hour. And if we were to convert that to si units, that is 2 m per second, we can multiply it, ok by 1000 m divided by 3600 seconds. Which when we do that, we end up with V one being equal to 60 m per second. Ok? We also know that V two equals 0.85 V one. We know that our distance is 18 m, ok? And we know that the mass of the bullet M equals 0.016 kg. Now, what do we know about work that relate that is related to any of the information we already have. Well, the only force acting on this bullet in the the bullet in this case is the drug force due to air due to the E sorry. And this force does work on the bullet. Which causes a change in its kinetic energy. Recall that work done is defined as a change in kinetic energy. OK. So if I put that in red here, put that in red since work done is defined as the change in kinetic energy, OK. Then by applying that idea, that means our work done due to friction is going to be equal to a half of MV two squared. OK? Because remember kinetic energy is equal to a half of MV squared. So that's our final kinetic energy. OK. Minus our initial kinetic energy half of MV one squared. We can even factor the out of more to rewrite this as a half of M multiplied by V two squared minus V one squared. Now, since that's the case, we know what V two V one and M are, we can substitute to find our force, our average force due to sorry, our average drug force due to air because no, that means then that the force is going to be equal to the negative value. OK? Of half of M multiplied by V two squared minus V one squared. OK. All divided by uh our distance deep. Now, if we substitute the values that we know that's going to be a half of 0.016 kg. OK. Multiplied by V two squared. So that's 60 m per second. All squared. OK. Midas V one squared. OK. Well, no, sorry we know that V two was 0.85 of V one. So that's 0.85 multiplied by 60 m per second squared. OK. Minus V one which is rightfully 60 m per second squared. OK. Some square rackets here and all of that is being divided by our distance which is 18 m. So now to figure that out, all we need to do is to substitute our values and thus be able to solve for our fictional force or for our average drug force. Now, when we do that, OK, when you put this into your calculator, you should find that you get the average drug force to be equal to 0.44 newtons, sorry, 444 newtons. And if we take that to two significant figures, then it's going to be equal to 0.44 newtons. In other words, the average drug drug force due to air on the bullet is 0.44 newtons. If we look back at our answer choices, that means a is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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A softball having a mass of 0.25 kg is pitched horizontally at 120 km/h. By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distance between the plate and the pitcher is about 15 m.

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