Question

1. A man sits in a cannon barrel and lights the fuse. A force of 6000 N propels him out of the barrel (which is 2.5 meters long) in a time of 0.35 seconds. The man has a mass of 85 kg.

1. How much work is done on the man by the cannon? Ignore the man’s weight.
2. What is the average power exerted on the man?
3. What is the man’s velocity as he leaves the cannon barrel?
4. How high above the cannon barrel does he rise during his flight?

Answer 1

a] Work = F*d = 6000*2.5 = 15000 J

b] Power exerted = work/time = 15000/0.35 = 42857 W

c] velocity v = sqrt(2KE/m) = sqrt(2*15000/85) = 18.786 m/s

d] Height h = v^2/2g = 18.786^2/(2*9.8) = 18 m

Answer 2

To solve this problem, we can use the equations for work, power, and kinematics.

First, we can find the work done on the man by the cannon using the formula:

Work = Force x Distance

where the force is the propelling force of 6000 N, and the distance is the length of the cannon barrel of 2.5 meters. Therefore:

Work = 6000 N x 2.5 m = 15000 J

Next, we can find the average power exerted on the man using the formula:

Power = Work / Time

where the work is 15000 J, and the time is 0.35 seconds. Therefore:

Power = 15000 J / 0.35 s = 42857.14 W

Note that this is the average power over the entire time of the man's flight, including the time spent inside the cannon barrel.

To find the man's velocity as he leaves the cannon barrel, we can use the equation of motion:

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity (which is zero), a is the acceleration, and s is the displacement. The acceleration is given by:

a = F / m

where F is the propelling force of 6000 N, and m is the man's mass of 85 kg. Therefore:

a = 6000 N / 85 kg = 70.59 m/s^2

The displacement is the length of the cannon barrel, which is 2.5 meters. Therefore:

v^2 = 0 + 2 x 70.59 m/s^2 x 2.5 m v^2 = 353.0 v = 18.8 m/s

Finally, we can find the height that the man reaches using the formula:

h = (v^2 / 2g)

where g is the acceleration due to gravity of 9.81 m/s^2. Therefore:

h = (18.8 m/s)^2 / (2 x 9.81 m/s^2) = 18.2 m

Therefore, the man reaches a height of 18.2 meters above the cannon barrel during his flight.