(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7....

Question

(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7.0 m/s² by means of the triceps muscle, as shown. Calculate

(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm

Accepted Answer

Welcome back. Everyone in this problem. Suppose an arm utilizing the triceps muscle accelerates a 3.7 kg weight at 7.1 m per second squared. Calculate the force exerted by the triceps muscle while ignoring arm mass for our answer choices. A says it's 123 newtons. B 232 newtons C 323 newtons and D 433 newtons. No. Here if we're trying to figure out the force, OK. The force exerted by the triceps muscle, then let's make a note of all the information we already have so far. OK. So so far we know that our triceps muscle is accelerating a 3.7 kg weight. So this weight here is equal to 3.7 kg and that weight is M OK. We also know that it does that at 7.1 m per second squared. So this acceleration is the acceleration due to translational motion, the linear acceleration. So we can say that this acceleration is going to be tangential to our circular motion. OK? Because remember if this is our circular motion, then our translational acceleration is tangent to that circuit. So our tangential acceleration then is 7.1 m per second squared. OK. No. Uh what else do we know? We also know that our arm based on our diagram is 32 centimeters long. So that means our radius R OK is 32 centimeters or in si units, 0.230 0.32 m sorry. And then we know that our distance or perpendicular distance from our force here at or axis of rotation. So that perpendicular distance is represent that using uh our with a perpendicular sign at the bottom and that perpendicular distance is 2.6 centimeters or in si units 2.6 multiplied by 10 to the negative 2 m. OK. So this is all the information that we're given so far. And from it, we're trying to figure out the force exerted by our triceps muscle, let's call that force F. No. What do we know about force? We're talking about circular motion here? Well, we know that our torque is measured as the rotational force applied to an object and the torque from the arm gives angular acceleration to the object only. Now, what do we know about torque and force? Well, recall, OK, recall that torque is actually defined as the force multiplied by the perpendicular distance. OK. Or the distance that's perpendicular to our applied force here. So if we're trying to find that force, that means the force is going to be equal to the torque divided by that perpendicular distance. We know the distance, but we don't know the torque. So if we can figure out the torque, then we should be able to figure out the force. Now, what else do we know about force? Well, again, like we said earlier, OK. So solving for our torque, sorry, not force. What else do we know about torque? Solving for a torque? The torque gives our angular acceleration and our torque is actually defined as the moment of inertia multiplied by that angular acceleration. Again, we we're not giving these things directly, but we know that our moment of inertia here for our object is equal to Mr R squared. OK. And we also know that our angular acceleration is equal to a tangential acceleration divided by that distance R. So if we use that idea, then this would imply that our torque is going to be equal to Mr squared multiplied by our tangential acceleration divided by R where we can factor out R to get M multiply or rather or tangential acceleration multiplied by M multiplied by R. OK. So this is what we know about our torque since we have a value for our torque. And we know what all of these variables are, we can substitute it into our expression for our force because no, since our force equals the torque divided by our perpendicular distance, it's going to be a and Mr divided by our perpendicular distance. I, if we substitute our values that we know here, we know a tangential acceleration is 7.1 m per second squared. The mass of our object or weight is 3.7 kg. And our distance, the length of our uh distance here of our arm is 0.32 m. And all of that is being divided by our perpendicular distance which we defined to be 2.6 multiplied by 10 to the negative 2 m. So to find this force, all we need to do is to evaluate this expression. Now, if you put this expression into your calculator, uh let me put it down here, then you should find that you get the force to be equal to you, the force to be equal to 323 newtons to three significant figures. Therefore, the force exerted by the triceps muscle is 323 newtons. C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Struggling with Physics?

(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7.0 m/s² by means of the triceps muscle, as shown. Calculate
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm
<IMAGE>

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Struggling with Physics?

(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7.0 m/s² by means of the triceps muscle, as shown. Calculate(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm<IMAGE>

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(II) The forearm in Fig. 10–57 accelerates a 3.6-kg ball at 7.0 m/s² by means of the triceps muscle, as shown. Calculate
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm
<IMAGE>