A forearm with a mass of 1.2kg supports a ball with a mass of 5.44 kg. The forearm is 0.050m long; it's perpendicular to the arm is 0.35m long, the center of gravity is at 0.15m from the elbow. Find the force exerted by rhe biceps and the force on the elbow joint.
I know this is just like any other problem with center of gravity and trying to find the forces on both ends supporting the ball, but there's only one support, the elbow, so that would be the fulcrum and even then, what does the forearm length have to do with it? I don't know how to set up the equation.
can someone pretty please help?
You need to know how far from the fulcrum, the hinge at the elbow, the biceps attaches to the forearm. Move your forearm up and down. You can feel that the biceps pulls up on the forearm well forward of the pivot at the rear of the elbow. That is the distance you can not do without.
So, how can I slove it, please?
To solve this problem, we need to understand the concept of moments and torque.
First, let's consider the forces acting on the forearm-ball system. There are two forces involved:
1. Force exerted by the biceps
2. Force exerted on the elbow joint.
When the system is in equilibrium, the sum of the moments about any point must be zero. In this case, we can choose the elbow joint as the reference point.
Now, let's set up the equation to find the force exerted by the biceps and the force on the elbow joint.
1. Force exerted by the biceps (Fb):
- This force is responsible for holding the forearm-ball system in equilibrium.
- To calculate this force, we need to consider the torque produced by the forearm and the torque produced by the ball.
- The torque produced by an object can be calculated by multiplying the force applied and the perpendicular distance from the point of rotation (fulcrum).
For the forearm:
- Torque produced by the forearm can be calculated as: T_forearm = (mass_forearm) * (acceleration_due_to_gravity) * (distance_from_fulcrum)
- Substituting the given values, we have: T_forearm = (1.2 kg) * (9.8 m/s^2) * (0.15 m)
For the ball:
- Torque produced by the ball can be calculated as: T_ball = (mass_ball) * (acceleration_due_to_gravity) * (distance_from_fulcrum)
- Substituting the given values, we have: T_ball = (5.44 kg) * (9.8 m/s^2) * (0.35 m)
Since the system is in equilibrium, the sum of the torques must be zero:
T_forearm + T_ball = 0
To calculate the force exerted by the biceps (Fb), we need to divide the total torque by the perpendicular distance from the point of rotation:
Fb = (T_forearm + T_ball) / (length_forearm)
2. Force on the elbow joint (Fe):
- The force on the elbow joint is equal in magnitude but opposite in direction to the force exerted by the biceps (Fb).
- So, Fe = -Fb
To summarize, the steps to find the force exerted by the biceps and the force on the elbow joint are as follows:
1. Calculate the torque produced by the forearm (T_forearm).
2. Calculate the torque produced by the ball (T_ball).
3. Calculate the force exerted by the biceps (Fb) using the equation Fb = (T_forearm + T_ball) / (length_forearm).
4. Calculate the force on the elbow joint (Fe) by taking the negative value of Fb: Fe = -Fb.