Question

Two balls a and b of masses 2m and 4m are in motion with velocities 2v and 4v respectively. what is the force needed to stop them in the same time

Answer 1

Answer:

1 : 4

Explanation:

Two balls a and b of masses 2m and 4m are in motion with velocities 2v and 4v respectively. what is the force needed to stop them in the same time

Let say in T time both balls are stopped

so Ball a mass = 2m  velocity = 2v

0 = 2v + aT

=> a = -2v/T

a = F/2m

=> 2v/T = F/2m

=> F = 4mv/T

Ball b mass = 4m  velocity = 4v

0 = 4v + aT

=> a = -4v/T

a = F/4m

=> 4v/T = F/4m

=> F = 16mv/T

=> F = 4(4mv/T)

Forces required are in ratio of 1 : 4  for a & B ball

Answer 2

Answer:

The force on b will be 4 times force on a.

Explanation:

Given that,

Mass of a ball = 2m

Mass of b ball = 4 m

Velocity of a ball = 2 v

Velocity of b ball = 4 v

We need to calculate the acceleration of ball a

Using equation of motion

$v= u+at$

Where, v = final velocity

u = initial velocity

a = acceleration

t = time

Put the value in the equation

$v=u+at$

$0=2v+a\times t$

$a=-\dfrac{2v}{t}$.....(I)

Negative sign shows the retardation

We need to calculate the acceleration of ball b

$0=4v+a\times t$

$a =-\dfrac{4v}{t}$.....(II)

Negative sign shows the retardation

We need to calculate the force

For ball a

$F=ma$

$F_{1}=2m\times\dfrac{2v}{t}$

$F_{1}=\dfrac{4mv}{t}$

For ball b

$F_{2}=4m\times\dfrac{4v}{t}$

$F_{2}=\dfrac{16mv}{t}$

$F_{2}=4F_{1}$

Hence, The force on b will be 4 times force on a.