Sir Dudley the Dextrous is loading cannons on top of the castle\\\'s tallest tow
ID: 1355651 • Letter: S
Question
Sir Dudley the Dextrous is loading cannons on top of the castle's tallest towers in preparation for an expected attack. He slips, and a 18.0 kg cannonball rolls to the edge of the tower (which has a perfectly horizontal surface), and falls to the ground below. It takes the cannonball 2.15 seconds to fall to the ground, and air resistence is negligible. How much work is done by gravity on the falling cannonball?
________J
During the fall, what is the average power transfer to the cannonball due to the force of gravity?
_________W
Explanation / Answer
Given that,
Mass of the ball = M = 18 Kg ;
time taken by the ball to fall on the ground = t = 2.15 s
Let Wg be the work done by the gravity on the ball.
From equation of motion, we know that,
S = ut + 1/2 a t2 ; In our case, S = H ( height from which ball is fired) ; u = 0 ; a = g = 9.8 m/s2 ; t = 2.15 s Putting the values we get:
H = 0 + 1/2 x 9.8 x (2.15)2 = 22.7 meters
We know from the defination of work, Work = Force x distance,
In this case Force = gravitational pull = M g = 18 x 9.8 = 176.4 N and distance = height = H = 22.7 m
So work done by the gravity will be: Wg = 176.4 x 22.7 = 4004.3 J
Hence, Wg = 4004.3 J.
(b) We know from the defination of Power:
Power = Work done / time
We have already calculated the workdone and time is provided. So putting in the values, we get:
Power = 4004.3/2.15 = 1862.5 Watts
Hence, Power = 1862.5 Watts.