Question

Two forces equal in magnitude and opposite in direction, acting on an object at two different points, form what is called a couple. Two antiparallel forces with equal magnitudes F1=F2=7.10 N are applied to a rod as shown in the figure (Figure 1) .

Part A
What should the distance l between the forces be if they are to provide a net torque of 7.00 N?m about the left end of the rod
l = m
Part B
Is the sense of this torque clockwise or counterclockwise?
Part C
Repeat part A for a pivot at the point on the rod where F? 2 is applied.
Part D
Repeat part B for a pivot at the point on the rod where F? 2 is applied.

Answer 1

The distance between the forces needs to be 0.99 m to provide a net torque of 7.00 N*m. The sense of the torque is counterclockwise. The same distance applies when the pivot is at the point where F2 is applied.

Step-by-step explanation:

For Part A, to calculate the distance l, we can use the formula T = F * l, where T is the torque and F is the force. Rearranging the equation, we have l = T / F. Plugging in the values T = 7.00 N*m and F = 7.10 N, we get l = 0.99 m.

For Part B, the sense of the torque can be determined by looking at the direction of rotation. If the rotation is clockwise, the torque is considered negative, and if the rotation is counterclockwise, the torque is considered positive. In this case, since the net torque is positive, the sense of the torque is counterclockwise.

For Part C, if the pivot is at the point where F2 is applied, the torque will be the same as in Part A, because the force and distance are still equal. Therefore, the distance l will still be 0.99 m.

For Part D, since the net torque is positive, the sense of the torque is counterclockwise, regardless of the location of the pivot.

Answer 2

To generate a net torque of 7.00 N·m about the left end of the rod by forces of 7.10 N, the distance between the forces should be 0.986 m, which results in a counterclockwise rotation. If the pivot is at the point where one of the forces is applied, the net torque is the same but due to only one force.

Step-by-step explanation:

When two forces equal in magnitude and opposite in direction (antiparallel) act on an object at different points, they form a couple, creating a torque. Torque, which is a measure of the tendency of a force to rotate an object about an axis, is defined by the equation T = F × l, where T is the torque, F is the force applied, and l is the distance between the forces, also known as the moment arm.

Part A: To solve for the distance l that will provide a net torque of 7.00 N·m about the left end of the rod, you can rearrange the formula to calculate the moment arm: l = T/F. Given that F1 = F2 = 7.10 N, you get l = 7.00 N·m / 7.10 N = 0.986 m.

Part B: The sense of this torque will be counterclockwise because when looking from the left end of the rod, the force on the right attempts to rotate the rod in a counterclockwise direction.

Part C: If the pivot point is at the point where F2 is applied, there will be no distance between the pivot and the force, thus no torque can be generated by F2. The net torque about this point only due to F1 would be 7.00 N·m (as the entire rod will act as the moment arm for F1).

Part D: The sense of the torque when the pivot is at the point where F2 is applied will remain counterclockwise, as F1 still tends to rotate the rod around the pivot in the same direction.