Question

A cannon ball of 2kg leaves the barrel of the cannon, with a velocity 100m/s. If the cannon weighs half tonn and moves through 0.5m, what is the resistance offered by the ground to the motion of the cannon​

Answer 1

Answer:

• Resistive force of 80 N will be offered by the ground., in the direction opposite to the motion of cannon after firing the ball.

Explanation:

Given,

Mass of cannon ball, m = 2 kg

Mass of cannon, M = half tonne = 500 kg

Final velocity of cannon ball, v = 100 m/s

Let, final velocity of cannon = V

Distance covered by cannon after firing the ball, s = 0.5 m

To find,

Resistive force offered by the ground to the motion of the cannon, F =?

Solution,

Initially both Cannon and ball would be at rest, therefore

Initial velocity of Cannon ball = Initial velocity of cannon = u = 0

Using law of conservation of momentum

→ m u + M u = m v + M V

→ m (0) + M (0) = ( 2 ) ( 100 ) + ( 500 ) V

→ 0 = 200 + 500 V

→ V = -200/500

→ V = -0.4 m/s

Now,

Let acceleration of cannon after firing the ball be a

then, After firing the ball cannon will have U = V = -0.4 m/s as initial velocity and it will cover a distance of s = 0.5 m to come to rest hence, final velocity will be V' = 0

Using third equation of motion for cannon

→ 2 a s = V'² - U²

→ 2 a ( 0.5 ) = ( 0 )² - ( -0.4 )²

→ a = -0.16  m/s²

Now, Using newton's second law of motion for cannon

→ F = M a

→ F = ( 500 ) · ( -0.16 )

→ F = -80 N

Therefore,

• A resistive force of 80 Newtons will be offered by the Ground, in the direction opposite to the motion of Cannon after firing the ball.