An athlete holds a 18.5 kg dumbbell in equilibrium as shown....

An athlete holds a 18.5 kg dumbbell in equilibrium as shown. Her flexor muscle exerts a force Ff perpendicular to the forearm. The muscle is attached to the forearm a distance df = 0.053 m from the elbow joint. The dumbbell is a distance dM = 0.29 m from the elbow joint. Ignore the mass and moment of inertia of her forearm relative to the dumbell mass. a. Draw a free-body-diagram of her forearm. b. Find the magnitude of the force Ff . c. Find the magnitude of the force applied by the upper arm bone to the forearm at the elbow joint. d. She begins to lift the dumbbell with an angular acceleration about the elbow joint 0.65 rad/s^2 . How much more force must her flexor exert now?

Transcript

00:01 So here we're starting with a free body diagram.

00:03 So we have the bar or the beam of the lower arm.

00:07 Now we have the mass acting on it of the weight.

00:11 So it's 18 .5 kilograms.

00:13 Now we want this in force.

00:14 We multiply it by g.

00:16 That's going to give us a force.

00:17 Kilograms times acceleration to give us the weight.

00:22 Now the muscle provides some force f upwards here.

00:27 And knowing, having done these problems, we know this force is going to be larger because of the moment.

00:32 And that's going to mean the force due to the bone here, i call it fb, is going to be downwards.

00:38 But if you assume the other direction you get a negative answer.

00:40 It just means you flip the direction.

00:43 We need an axis, so x along the beam and y upwards by convention.

00:49 We also need our dimensions.

00:51 So between the bone and the force from the muscle 0 .053 meters and to the end of the arm 0 .29 meters.

01:03 So the first thing we're going to look at is moments.

01:08 And that's in part b, saying the sum of moments is equal to zero.

01:15 So we can take counterclockwise to be positive moments.

01:18 And we know knowing a moment is a force times a distance.

01:22 Let's look at moments about our origin.

01:25 If we take that force b acts right at that point, so it has no moment.

01:29 So that means we have an equation in one unknown ff, which we can solve for directly.

01:34 We see ff rotates counterclockwise.

01:36 That's a positive moment.

01:38 The weight is a negative moment.

01:41 And we're not including the mass of the arm or anything, so this is the only force we need to look at.

01:48 So for the force from the muscle ff times the distance to the origin where we're taking moments 0 .053.

02:00 And then the force of the weight, the 18 .5, 9 .81 meters per second for the acceleration due to gravity.

02:12 And then we also need the distance 0 .29 meters equal to zero...

Question

Please give Ace some feedback