Question

An archer pulls her bowstring back 0.400m by exerting a force that increases uniformly from zero to 230N. (b) How much work does the archer do on the string in drawing the bow?

Answer 1

The archer does 23.0 joules of work on the bowstring in drawing the bow, calculated using the average force and the distance over which it's exerted.

Step-by-step explanation:

The question concerns the amount of work done by the archer when she draws the bow. Work in physics is defined as the product of the force exerted on an object and the distance over which that force is applied. When the force is applied uniformly, the work done can be calculated using the average force times the distance. In this case, the archer exerts a force that increases uniformly from zero to 230N over a distance of 0.400m. Since the work done is equivalent to the area under the force-distance curve, which forms a triangle in the case of a uniform force, the work can be calculated as (1/2) × force × distance. Applying this formula:

Calculate the average force: (0N + 230N) / 2 = 115N (average force).

Calculate the work done: (1/2) × 115N × 0.400m = 23.0J (work done).

Therefore, the archer does 23.0 joules of work on the bowstring in drawing the bow.

Answer 2

The work done by the archer on the bowstring is 46 J.

Step-by-step explanation:

The work done by the archer on the bowstring can be calculated using the formula:

Work = Force * Distance

In this case, the force exerted by the archer increases uniformly from zero to 230N and the distance pulled back by the bowstring is 0.400m. Therefore, the work done by the archer on the string is:

Work = (230N * 0.400m)/2 = 46 J