Find the net torque on the wheel in the figure below about the axle through O perpendicular to the page, taking a = 5.00 cm and b = 23.0 cm. (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.) f1= 10 f2= 9 f3=12
To find the net torque on the wheel, we first need to determine the torque produced by each force and then add them together.
Torque is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of rotation to the line of action of the force. Mathematically, the torque (τ) is given by τ = F * d, where F is the force and d is the distance.
In this case, we have three forces (f1, f2, and f3) acting on the wheel. Let's calculate the torque produced by each force:
1. Torque produced by f1:
The magnitude of the force f1 is 10 units. The perpendicular distance (d1) from the point of rotation O to the line of action of f1 is given as a = 5.00 cm. Since the force f1 is perpendicular to the page, the torque produced by f1 is τ1 = f1 * d1 = 10 * 5.00 cm.
2. Torque produced by f2:
The magnitude of the force f2 is 9 units. The perpendicular distance (d2) from the point of rotation O to the line of action of f2 is given as b = 23.0 cm. Since the force f2 is also perpendicular to the page, the torque produced by f2 is τ2 = f2 * d2 = 9 * 23.0 cm.
3. Torque produced by f3:
The magnitude of the force f3 is 12 units. The perpendicular distance (d3) from the point of rotation O to the line of action of f3 is given as b = 23.0 cm. Since the force f3 is perpendicular to the page, the torque produced by f3 is τ3 = f3 * d3 = 12 * 23.0 cm.
Now that we have calculated the torque produced by each force, we can find the net torque by adding them together:
net torque = τ1 + τ2 + τ3
Here, we need to consider the directions of the torques. The positive direction is counterclockwise, so we need to assign a positive sign to torques that act counterclockwise and a negative sign to torques that act clockwise.
Assuming all the forces act counterclockwise, the net torque will be:
net torque = τ1 + τ2 + τ3
Finally, substitute the calculated values to find the net torque.