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
= 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.