Equilibrium problem (torque and forces)

In summary, the problem involves finding the values of vector T, vector R, and θ when the total gravitational force on the body is 685 N. The solution involves using the equations for sum torque, sum forces in the y-direction, and sum forces in the x-direction. After solving for T in sum torque = 0, it is substituted into the other two equations to solve for R and θ. The solution process may be difficult and messy, but it is important to continue working through it.
  • #1
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Homework Statement


When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure (a). The total gravitational force on the body, vector F g, is supported by the force vector n exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure (b), where vector T is the force exerted by the Achilles tendon on the foot and vector R is the force exerted by the tibia on the foot. Find the values of vector T , vector R , and θ when vector F g = 685 N. (Do not assume that vector R is parallel to vector T .)
http://img399.imageshack.us/img399/7326/p816yx9.th.gif [Broken]

Homework Equations


1) Sum torque = 0 : (0.07m*T) - (0.18m*685N*cos theta) = 0.
2) Sum forces in y-direction = 0: 685N + (T*cos theta) - (R*cos 15) = 0
3) Sum forces in x-direction = 0: (R*sin 15) - (T*sin theta) = 0


The Attempt at a Solution


I solved sum torque = 0 to get T= 1761.43 cos theta.

Put T into sum forces in y-direction to get
R = [1761.43 (cos theta)(sin theta)]/sin 15

Then put this into sum forces in x-direction. It got really messy, I can post what I have but am not sure how to solve this. Am I going in the right direction here?
 
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  • #2
Anyone? I'm trying to finish this bad boy for tomorrow and would appreciate the help.
 
  • #3


I would like to point out that in order to accurately solve this problem, we need to make some assumptions about the physical properties of the foot and leg. For example, we would need to know the length and strength of the Achilles tendon and the tibia bone in order to accurately determine the values of T and R. Additionally, the angle theta may vary depending on the individual's anatomy and level of exertion while standing on tiptoe.

That being said, based on the given information and equations, your approach seems to be correct. However, I would suggest breaking down the equations further and solving for theta first, as it is a common variable in all three equations. Once you have solved for theta, you can plug that value into the other equations to solve for T and R. This will make the calculations less messy and more manageable. Additionally, make sure to check the units of your final answer to ensure they are in the correct units (e.g. Newtons for force and degrees for angle).

Overall, this is a good problem to practice using torque and force equations in a real-life scenario. Keep up the good work!
 

What is an equilibrium problem?

An equilibrium problem is a type of physics problem that deals with balancing forces and torques on an object. In these problems, the goal is to determine the state of balance or equilibrium of an object, which can be either static (not moving) or dynamic (moving at a constant velocity).

What is torque?

Torque is a measure of the rotational force applied to an object. It is calculated by multiplying the force applied to an object by the distance from the point of rotation to the point where the force is applied. Torque is often measured in units of Newton-meters (N·m) or foot-pounds (ft·lb).

How do you determine the net torque on an object?

The net torque on an object is determined by summing the individual torques acting on the object. This is done by taking into account both the magnitude of the force and the distance from the point of rotation for each force. If the net torque is equal to zero, the object is in rotational equilibrium.

What are the conditions for rotational equilibrium?

For an object to be in rotational equilibrium, two conditions must be met: 1) the net torque acting on the object must be equal to zero, and 2) the net force acting on the object must also be equal to zero. This means that the object is either not moving or is moving at a constant rotational velocity.

How do you solve equilibrium problems?

To solve an equilibrium problem, you must first draw a free body diagram to identify all the forces and torques acting on the object. Then, apply the conditions for rotational equilibrium to set up equations and solve for any unknown quantities. It is important to keep track of the direction and magnitude of forces and torques to ensure an accurate solution.

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