Help with Compression forces

[staz87]

Homework Statement

The person in Figure P4.51 weighs 160 lb. Each crutch makes an angle of = 18.0° with the vertical (as seen from the front). Half of the person's weight is supported by the crutches, the other half by the vertical forces exerted by the ground on his feet.

find the magnitude of the compression force supported by each crutch (lbs)

Homework Equations

F=mg
Ax=Acos(18)
Ay=Asin(18)

The Attempt at a Solution

I broke down the 40 lbs being supported by each crutch. I found the Weight in the y direction to be 38.04 lbs I entered this in and the site says I am within 10% of the correct answer. I figured the normal force for this would be 40 lbs, but I am unsure as to how the forces interact to form a compression force. Is it not the supported weight + the normal force? Help greatly appreciated!

 

[anathema]

Hello,

You are on the right track! The normal force is actually the force that the ground exerts on the person's feet to support their weight. In this case, since half the person's weight is being supported by the crutches, the normal force would be half of the person's weight (80 lbs). The compression force is the force that the crutches exert on the person's arms to support their weight. This force is equal and opposite to the normal force, so it would also be 80 lbs for each crutch.

To find this using the equations you listed, you can use the fact that the sum of forces in the y direction must equal zero (since the person is not accelerating in the y direction). So you can set the weight in the y direction equal to the normal force plus the force exerted by the crutch in the y direction. This would look like:

Fy = 0 = N + Asin(18)

Solving for N (normal force) would give you 80 lbs. Then, since the force exerted by the crutch is equal and opposite to the normal force, the compression force would also be 80 lbs.

I hope this helps! Let me know if you have any other questions.

 

[m2003]

First, let's clarify the difference between tension and compression forces. Tension forces occur when an object is being pulled or stretched, while compression forces occur when an object is being pushed or compressed. In this case, the crutches are exerting a compression force on the person, as they are supporting his weight and pushing against him.

To find the magnitude of the compression force supported by each crutch, we can use the concept of equilibrium. Since the person is standing still, the forces acting on him must be balanced. This means that the vertical forces (in the y-direction) must add up to zero.

We know that half of the person's weight (80 lbs) is being supported by the crutches, and the other half is being supported by the ground. This means that the normal force exerted by the ground on each foot is also 80 lbs.

Now, let's look at the forces acting on the person in the y-direction. We have the weight (160 lbs) acting downwards, and the normal force (80 lbs) acting upwards. The crutches are also exerting a vertical force, which we can break down into its x and y components using trigonometry. The x-component of the crutch force will cancel out with the x-component of the weight, leaving only the y-components to add up to zero.

So, we can set up the following equation:

80 lbs + A*sin(18°) = 160 lbs

Solving for A, we get A = 160 lbs / sin(18°) = 467.85 lbs.

Since this is the total force exerted by both crutches, the magnitude of the compression force supported by each crutch would be half of this value, or approximately 233.93 lbs.

Hope this helps!