Question

For a home repair job you must turn the handle of a screwdriver 32 times.

Part A
If you apply an average force of 15 N tangentially to the 2.0-cm-diameter handle, how much work have you done?

Answer 1

To calculate the work done, use the formula W = Fd, where F is the force applied and d is the distance covered by the force. The distance can be found by calculating the circumference of the handle, which is equal to 2π times the diameter. In this case, the work done is approximately 1.89 Nm.

Step-by-step explanation:

To calculate the work done, we need to first find the distance over which the force is applied. Since the handle of the screwdriver is turned 32 times, and each turn requires a complete revolution, the distance covered by the force is equal to the circumference of the handle. The circumference can be calculated using the formula C = πd, where d is the diameter of the handle. Therefore, the distance is 2π(2.0 cm), or approximately 12.57 cm. To convert this to meters, divide by 100, resulting in a distance of 0.1257 m.

The work done is given by the formula W = Fd, where F is the force and d is the distance. Plugging in the values, we get W = (15 N)(0.1257 m) = 1.8855 Nm, or approximately 1.89 Nm.