Moment of force and static equilibrium

In summary, the problem involves an individual holding a 3 kg ball in static equilibrium, with the biceps brachii creating a tension force at a 2 cm distance from the elbow joint. The forearm has a mass of 1.5 kg and its center of mass is 18 cm from the elbow joint. The distance from the elbow joint to the point where the ball is held is 45 cm. Using the equations f=ma and static equilibrium, the magnitude of the tension running through the biceps brachii is found to be approximately 794.61 N. However, the angle at which the biceps is flexed (115°) needs to be taken into account using an equation that relates force and torque.
  • #1
lalm22
1
0
1) Problem:
An individual holds a ball of mass 3 kg in his hand in static equilibrium. The biceps brachii attaches a distance of 2 cm from the centre of rotation of the elbow joint, and the muscle's line of action is directed at an angle of 115° counter clockwise from the forearm. The forearm has a mass of 1.5 kg. The forearm's centre of mass is located a distance of 18 cm from the elbow joint. The distance from the elbow joint to the point at which the ball is held in the individual's hand is 45 cm. Assuming that the biceps brachii is the only muscle contributing to elbow flexor moment, what is the magnitude of the tension running through the biceps brachii?

http://imgur.com/1GQ3nNv

2) Relevant equations:

f=ma, Static Equilibrium: Em = 0

3) My solution
I know that i have to convert the mass of the forearm and the weight to Newtons, but what do I do with the angle. Fb = force biceps:

-29.43(0.45) - 14.715(0.18) + Fb(0.02) = 0
fb = 794.61

However, I can't figure out when to incorporate the angle (115) at which the biceps is flexed :/
 
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  • #2
There is an equation that relates the angle at which the force is exerted and the torque that will result from this force. This equation can be easily found. I don't see it in the introductory physics formulay... I'm sure that is for a reason, though.
 
  • #3
F=ma is always relevant, but for this problem there are other equations you will need to know. You seem to be ill-prepared to solve this type of problem, but you can remedy that by checking out the Wikipedia articles on torque and moment of inertia. Once you are able to list the relevant equations I can do more to help you.
 

1. What is a moment of force?

A moment of force, also known as torque, is a measure of the force's ability to rotate an object around an axis. It is the product of the force applied and the perpendicular distance from the axis to the line of action of the force.

2. How is moment of force calculated?

The moment of force is calculated by multiplying the magnitude of the force by the perpendicular distance from the axis to the line of action of the force. The formula for moment of force is M = F x d, where M is the moment of force, F is the magnitude of the force, and d is the perpendicular distance.

3. What is static equilibrium?

Static equilibrium is a state where all forces acting on an object are balanced, resulting in no net force or movement of the object. This means that the object will remain at rest or in a constant state of motion.

4. How do you determine if an object is in static equilibrium?

An object is in static equilibrium if the sum of all the forces acting on it is equal to zero and the sum of all the moments of force acting on it is also equal to zero. This means that there is no net force or moment of force causing the object to move or rotate.

5. How can moments of force be used to maintain static equilibrium?

In order to maintain static equilibrium, the moments of force acting on an object must be balanced. This can be achieved by adjusting the magnitude or direction of the forces acting on the object, or by changing the object's position relative to the axis of rotation. By carefully balancing the moments of force, an object can be held in a state of static equilibrium.

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