Solving Torque/Force Problem: Find F & R

  • Thread starter RileyAllen
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In summary, the problem involves a person holding a 12.0-kg dumbbell in a static equilibrium position, with the biceps muscle attached at a distance of 4.0 cm from the joint and the dumbbell at a distance of 45 cm from the joint. The weight of the dumbbell is represented by W. The task is to find the upward force exerted by the biceps on the forearm (F) and the downward force on the upper arm at the joint (R). Using the equations W=mg, T=rF, and downward torque= mg(1/2 l) + mg(l), the attempt at a solution involved calculating the weight of the dumbbell as 117.6N, converting
  • #1
RileyAllen
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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?
 
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  • #2
RileyAllen said:

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?
 
  • #3


I would like to commend you for your attempt at solving this problem. However, it seems that there may be some errors in your calculations. First, the weight of the dumbbell should be calculated using the equation W=mg, where m is the mass of the dumbbell and g is the acceleration due to gravity. In this case, the mass is given as 12.0 kg, so the weight should be 117.6 N, not millinewtons (mN).

Next, the downward torque equation you used is incorrect. The correct equation for downward torque in this case would be mg(l+1/2d), where l is the distance from the joint to the dumbbell and d is the distance from the joint to the biceps muscle attachment. Plugging in the values, we get a downward torque of 117.6(0.45+0.5*0.04)=57.024 Nm.

Since the system is in static equilibrium, the upward torque must be equal to the downward torque. Therefore, the upward force F exerted by the biceps on the forearm can be calculated using the equation F=T/r, where T is the torque and r is the distance from the joint to the biceps muscle attachment. In this case, F=T/d=57.024/0.04=1425.6 N.

To find the downward force R on the upper arm, we can use the equation R=W-F, where W is the weight of the dumbbell and F is the upward force exerted by the biceps. Plugging in the values, we get R=117.6-1425.6=-1308 N.

Therefore, the correct answers for parts a and b are F=1425.6 N and R=-1308 N, respectively. I hope this helps clarify the solution for you. Keep up the good work!
 

1. What is torque and how is it related to force?

Torque is the measure of a force's ability to rotate an object around an axis. It is calculated by multiplying the force applied by the distance from the axis of rotation to the point of application. In other words, torque is a force that causes an object to rotate.

2. How do you solve for force and torque in a problem?

To solve for force and torque, you need to have the values of the distance from the axis of rotation, the angle of rotation, and the mass of the object. Then, you can use the formula F = ma to find the force and the formula T = Frsinθ to find the torque. It is important to use the correct units and pay attention to the direction of the force and torque vectors.

3. Can you solve torque and force problems without knowing the angle of rotation?

No, the angle of rotation is a crucial component in calculating torque. Without it, the torque formula cannot be used and the problem cannot be solved accurately. It is important to always have all the necessary information before attempting to solve a torque and force problem.

4. Are there any real-world applications of torque and force?

Yes, torque and force are fundamental concepts in physics and have many real-world applications. For example, they are important in engineering and construction, as they determine the stability and strength of structures. They are also used in sports, such as in the calculation of the force needed to hit a golf ball a certain distance.

5. How can I check if my solution to a torque and force problem is correct?

One way to check if your solution is correct is to use the principle of conservation of energy. In a torque and force problem, the initial and final energies should be equal. You can also double-check your calculations and units to ensure they are correct. If you are still unsure, you can consult with a teacher or use online resources to verify your solution.

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