A foot pushes against the ground with a force of 777 N in the vertical direction with a perpendicular displacement of 0.125 m away from the COM and 850 N in the horizontal direction with a perpendicular displacement of 0.025 m away from the COM. If the calf muscle pulls with a 1658 N force at a 75° angle relative to the positive horizontal and acts 0.125 m away from the COM in the vertical direction and 0.025 m away from the COM in the horizontal direction, what is the net torque on the foot? If the foot has a moment of inertia of 0.0042 kgm2 ,what is the angular acceleration of the foot?

To find the net torque on the foot, we need to calculate the individual torques generated by each force and then sum them up.

1. Start by calculating the torque generated by the vertical force of 777 N. Torque is defined as force multiplied by the perpendicular distance from the point of rotation. In this case, the perpendicular distance is given as 0.125 m. The torque is calculated as:

Torque_1 = Force_1 * Distance_1 = 777 N * 0.125 m

2. Next, calculate the torque generated by the horizontal force of 850 N. The perpendicular distance for this force is given as 0.025 m. Calculate the torque as:

Torque_2 = Force_2 * Distance_2 = 850 N * 0.025 m

3. Now, calculate the torque generated by the calf muscle pull of 1658 N at a 75° angle relative to the positive horizontal. To find the perpendicular distance, you can use trigonometry. The vertical perpendicular distance is given as 0.125 m and the horizontal perpendicular distance is given as 0.025 m. The perpendicular distance for the calf muscle pull can be calculated using the sine of the angle as follows:

Vertical perpendicular distance = 0.125 m * sin(75°)
Horizontal perpendicular distance = 0.025 m * sin(75°)

Now, calculate the torque as:

Torque_3 = Force_3 * Distance_3 = 1658 N * (Vertical perpendicular distance + Horizontal perpendicular distance)

4. Finally, sum up the individual torques to find the net torque:

Net Torque = Torque_1 + Torque_2 + Torque_3

To find the angular acceleration of the foot, we can use the equation:

Net Torque = Moment of Inertia * Angular Acceleration

Rearranging the equation gives:

Angular Acceleration = Net Torque / Moment of Inertia

Substitute the values into the equation to find the angular acceleration.