Solving Torque/Force Problem: Find F & R

[RileyAllen]

Homework Statement

A person holds a 12.0-kg dumbbell in his hand with his forearm in the horizontal position as shown in Figure 1. The biceps muscle is attached a distance d=4.0 cm from the joint and the dumbbell is a distance l=45 cm from the joint. This system is in static equilibrium. It is reduced to a simple system of rods with the forces acting as shown in Figure 1. The mass of the forearm is neglected. W is the weight of the dumbbell.

a. Find the upward force, F, exerted by the biceps on the forearm.
b. Find the downward force on the upper arm, R, acting on the joint.

Homework Equations

W=mg
T=rF so F=T/r
Downward torque= mg(1/2 l) + mg(l)

The Attempt at a Solution

I got the weight of the dumbbell to be 117.6. I converted d to .04 m and l to .45 m.
Using down torque equation I got 79.38 mN, and since the system is in static equilibrium, the upward force should be the same.
The answer I have is incorrect. Can someone please explain to me why?

 

[LowlyPion]

Homework Statement

A person holds a 12.0-kg dumbbell in his hand with his forearm in the horizontal position as shown in Figure 1. The biceps muscle is attached a distance d=4.0 cm from the joint and the dumbbell is a distance l=45 cm from the joint. This system is in static equilibrium. It is reduced to a simple system of rods with the forces acting as shown in Figure 1. The mass of the forearm is neglected. W is the weight of the dumbbell.

a. Find the upward force, F, exerted by the biceps on the forearm.
b. Find the downward force on the upper arm, R, acting on the joint.

Homework Equations

W=mg
T=rF so F=T/r
Downward torque= mg(1/2 l) + mg(l)

The Attempt at a Solution

I got the weight of the dumbbell to be 117.6. I converted d to .04 m and l to .45 m.
Using down torque equation I got 79.38 mN, and since the system is in static equilibrium, the upward force should be the same.
The answer I have is incorrect. Can someone please explain to me why?

Consider the sum of the Torques about the joint.

For the system to be in equilibrium doesn't the upward force of the bicep over it's lever arm need to equal the downward force of the 117.6N of the weight at the end of the forearm?