Question

You are doing a bicep curl with a 15lb dumbbell, and your forearm is 15 inches long. During the eccentric portion of the curl, you extend the elbow from 90° to 180°. How much mechanical work is the dumbbell doing about the elbow during this motion?

Answer 1

The work done

Answer 2

To calculate the mechanical work done by the dumbbell during the eccentric portion of the curl, we need to consider the change in potential energy. The work done is equal to the change in potential energy.

The potential energy of an object in this context can be calculated using the formula:

Potential energy = mass * gravitational acceleration * height

In this case, the mass of the dumbbell is 15 lb, and the height is the change in the vertical position of the dumbbell during the eccentric portion of the curl. To calculate the change in height, we need to determine the distance the weight travels.

Given that the forearm length is 15 inches, and the elbow extends from 90° to 180°, we can use trigonometry to calculate the change in height.

Using the formula: Change in height = forearm length * (1 - cos(angle in radians))

First, we convert the angle from degrees to radians: angle in radians = angle in degrees * (pi / 180)

Let's calculate the change in height:

angle in degrees = 180° - 90° = 90° angle in radians = 90 * (pi / 180) = pi / 2

Change in height = 15 * (1 - cos(pi / 2)) Change in height = 15 * (1 - 0) Change in height = 15 inches

Now, we can calculate the mechanical work done by the dumbbell:

Work = Potential energy = mass * gravitational acceleration * height

Given that gravitational acceleration is approximately 32.2 ft/s^2, we need to convert the height from inches to feet:

Height in feet = Change in height / 12

Work = 15 lb * 32.2 ft/s^2 * (15 inches / 12) feet Work = 15 * 32.2 * 15 / 12 Work = 604.25 ft-lb

Therefore, the mechanical work done by the dumbbell about the elbow during the eccentric portion of the curl is approximately 604.25 ft-lb.