A person exerts a horizontal force of F = 179 N in the test apparatus shown in the drawing. (h = 0.35 m.) Find the horizontal force M that his flexor muscle exerts on his forearm. The distance between the fexor muscle and the elbow joinf is .051 m

(179*.35)/.051=1228.4313

Without a figure or drawing, it is not possible to understand. Sorry.

To solve this problem, we need to find the horizontal force M that the person's flexor muscle exerts on his forearm. We can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.

The first step is to calculate the acceleration of the person's forearm. We can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration.

Since the problem does not provide the mass of the forearm, we can assume it to be the same as the force applied (F = 179 N). Therefore, we can simplify the equation to a = F/m.

Next, we need to calculate the acceleration. We can use the equation a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time.

However, the problem does not provide any information about velocity or time. Therefore, we can assume that the velocity of the forearm is initially zero and the time taken is 1 second for simplicity.

So, Δv = 0 m/s (initial velocity) and Δt = 1 s.

Since the change in velocity is zero, the acceleration (a) will also be zero. Hence, the person's forearm will not accelerate.

Now, we need to find the force exerted by the flexor muscle (M) on the forearm.

We can use the equation F = ma again, but this time the mass (m) is the mass of the forearm plus the flexor muscle. Let's call it M_f.

Therefore, the equation becomes F = M_f * a.

Since the acceleration (a) is zero, the force (F) exerted by the muscle on the forearm will also be zero. Just to be clear, the muscle does not exert any horizontal force on the forearm when there is no acceleration.

So, the horizontal force M that the person's flexor muscle exerts on his forearm is zero.

To find the horizontal force M that the person's flexor muscle exerts on his forearm, we can use the concept of torque. Torque is the product of a force and its perpendicular distance from a pivot point. In this case, the pivot point is the elbow joint.

First, we need to calculate the torque caused by the person's exerted force F. The torque (τ) is given by the formula:

τ = F * d

Where F is the applied force and d is the perpendicular distance between the line of action of the force and the pivot point.

In this case, the perpendicular distance between the line of action of the force and the pivot point is the distance between the flexor muscle and the elbow joint, which is 0.051 m.

Substituting the given values, we have:

τ = 179 N * 0.051 m
≈ 9.129 N·m

Now, since torque is equal to the product of the force and its perpendicular distance, we can set up another equation involving the torque exerted by the flexor muscle (M) and its perpendicular distance (h = 0.35 m) from the elbow joint:

τ = M * h

Substituting the value of torque (τ) from the first equation, we have:

9.129 N·m = M * 0.35 m

Now, solving for M:

M = 9.129 N·m / 0.35 m
≈ 26.083 N

Therefore, the horizontal force M that the person's flexor muscle exerts on his forearm is approximately 26.083 N.