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Calculating Force Based On Newton's Second Law Of Motion (4)

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Question 1:

A ball of mass 5.0 kg hits a smooth vertical wall normally with a speed of 2 ms-1 and rebounds with the same speed. Determine the impulse experienced by the ball.

Solution:

From Newton's second law of motion, Force is directly proportional to the rate of change of momentum.

I.e. F = (mv - mu)/t

Ft = mv - mu

Where Ft = Impulse (I)

I = mv - mu

Since the speed with which the ball hits the wall is same as the speed it rebounds with, there is no change in momentum.

Therefore, Impulse (I) is zero, there is no impulse.

Question 2.

A force acts on a body for 0.5 s changing its momentum from 16.0 kgms-1 to 21.0 kgms-1. Calculate the magnitude of the force.

Solution:

From Newton's second law of motion,

Force equals the rate of change of momentum,

F = (mv - mu)/t

Where

mv = final momentum, mu = initial momentum.

F = (21 - 16)/0.5

= 5/0.5

= 10 N

The magnitude of the force is 10 Newtons

Question 3:

A stationary object of mass 4 kg is set in motion by a net force of 50 N. If the object attains a speed of 5 ms-1 in time. Calculate the value of t.

Solution:

From the equation of force,

F = m (v-u)/t

Therefore, restating the formula,

t = m(v - u)/F

Given: mass of object m = 4 kg, final velocity v = 5 ms-2, initial velocity u = 0, Force F = 50 N, t = ?

Hence,

t = 4 x (5 - 0)/50

= 20/50

t = 0.4s

Question 3.

A force of 100 N is used to kick a football of mass 0.8 kg. Find the velocity with which the ball moves if it takes 0.8s to be kicked.

Solution:

Using the force equation

F = m (v - u)t

100 = 0.8 (v - 0)/0.8

v = 100

The velocity with which the ball moves is 100 ms-1        [Note: initial velocity, u = 0]