Calculate the power output in watts and horsepower of a shot-putter who takes 1.20 s to accelerate the 7.27-kg shot from rest to 14.0 m/s, while raising it 0.800 m. (Do not include the power produced to accelerate his body.)

Solution 46 PE

Step 1 of 5</p>

The power output of the shot-putter can be calculated by finding the sum of work done in raising the shot put to 0.8 m which is nothing but the gravitational potential energy of the shot put at that height (W1 ) and work done in accelerating the shot put from rest to 14.0 m/s (W2)

Step 2 of 5</p>

The gravitational potential energy PEs of the shot put at a height h from the ground is

Where, g = acceleration due to gravity = 9.8 m/s2

m = mass of the shot put = 7.27 kg

h = distance from the ground = 0.8 m

This potential energy is equal to the work done(W1) in raising the shot put.

So, Substitute 7.27 kg for m, 9.8 m/s2 for g, 0.8 m for h

= ( 7.72 ) (9.8) (0.8)

W1 = 60.52 J

Step 3 of 5</p>

The work done (W2) can be calculated using the Work - Energy Theorem which states that the net work done by the system is equal to change in the quantity ½ m v2.

Here, m = mass of the sprinter = 7.27 kg v = final velocity = 14.0 m/s vo= initial velocity = 0 m/s

Substituting 7.27 kg for m, 14.0 m/s for v, 0 m/s for vo

=

= ( 0.5) (7.27) (196)

W2 = 712. 46 J

Step 4 of 5</p>

The power output (P) of the shot putter is then by definition the amount of total work done in the given time.

Here, t = 1.20 s

Now, the total work done by the shot putter is,

= 772.98 J

Now,

=

= 644.15 W

Step 5 of 5</p>

Conversion of power in watts to horsepower .

1 horsepower = 746 W

So, 644.15 W = 644.15 W

= 0.86 horsepower

Therefore, the power output of the shot putter is 644.15 in watts or 0.86 horsepower.