Help in solving momentum and impulse physics problems
Momentum - The product of mass and its linear velocity is called linear momentum of the body.Its unit is kgms-1.
1. Calculate the momentum of a body of mass 5 kg having the following velocities:
a. 10m/s b. -20m/s c. zero
Momemtum = mass x velocity
a. velocity, v = 10m/s
Momentum, p = mv = 5 x 10 =50kgm/s
b. v = -20m/s
p = 5 x -20 = -100kgm/s
c. v = 0 m/s
p = 5 x 0 = 0
2.. What force acting on a mass of 15kg for one minute can change its velocity from 10ms-1 to 50ms-1?
vi = 10m/s, vf = 50m/s, t = 60s, m = 15kg, a = ?, F = ?
50 = 10 + 60a
60a = 40
a = 40/60 = 2/3 ms-2
Force = ma = 15 x 2/3 = 10N
3.. A bullet of mass 0.01kg moving with a velocity 100m/s strikes a wooden plank of thickness 0.5m. and emerges with a velocity 30m/s. Find the resistance offered by the plank.
m = 0.01kg, vi = 100m/s, vf = 30m/s, S = 0.5m, a = ?, F = ?
vf2 - vi2 = 2aS
302 - 1002 = 2 x a x 0.5
a = -9100m/s2
Force = ma = 0.01 x 9100 = 91N
Help in Momentum problems in Physics : Impulse
The force acting for a very short time is called an impulsive force. It is measured as the rate of change in momentum.
Impulse of a force is the product of the force and the time during which the force acts on the body
Impulse = Force x time
I = F x dt
1. A batman hits back a ball straight in the direction of the bowler without changing its initial speed of 12 m/s. If the mass of the ball is 0.15kg, determine the impulse imparted to the ball.
vi = 12 m/s, vf = -12m/s, m = 0.15kg, I = ?
I = mvf - mvi = m(vf - vi) = 0.15 (-12 -12) = -3.6N
2. Some tennis players can serve the ball at a speed of 55m/s. The tennis ball has a mass of 60g. In an experiment it is determined that the ball is in contact with the racket for 25ms during the serve. Calculate the average force exerted by the racket on the ball.
The change in momentum of the ball as a result of the serve is
0.060 x 55 = 3.3kgm/s.
By the impulse momentum equation, the change in momentum is equal to the impulse of the force.
Since impulse is the product of force and time, F*t = 3.3Ns
Here t = 0.025s
Thus F = 3.3/0/025 = 132N
3. A golfer hits a ball of mass 45g at a speed of 40m/s. The golf club is in contact with the ball for 3.0ms. Calculate the average force exerted by the club on the ball.
m = 0.045kg, vi = 0, vf = 40m/s
Force = ma = m (vf - vi)/t
= (0.045 x 40)/.003