Impulse is the product of the net force and the time interval for which the force acts. Impulse is defined as:
However, from Newton's Second Law, we know that
Therefore,
Impulse is equal to the change in momentum of an object. From this equation we see, that for a given change in momentum,
is fixed. Thus, if
is reduced,
must be increased (i.e. a smaller resultant force must be applied for longer to bring about the same change in momentum). Alternatively if
is reduced (i.e. the resultant force is applied for a shorter period) then the resultant force must be increased to bring about the same change in momentum.
A 150 N resultant force acts on a 300 kg trailer. Calculate how long it takes this force to change the trailer's velocity from 2 m
s
to 6 m
s
in the same direction. Assume that the forces acts to the right.
The question explicitly gives
the trailer's mass as 300 kg,
the trailer's initial velocity as 2 m
s
to the right,
the trailer's final velocity as 6 m
s
to the right, and
the resultant force acting on the object
all in the correct units!
We are asked to calculate the time taken
to accelerate the trailer from the 2 to 6 m
s
. From the Law of Momentum,
Thus we have everything we need to find
!
Choose right as the positive direction.
It takes 8 s for the force to change the object's velocity from 2 m
s
to the right to 6 m
s
to the right.
A cricket ball weighing 156 g is moving at 54 km
hr
towards a batsman. It is hit by the batsman back towards the bowler at 36 km
hr
. Calculate
the ball's impulse, and
the average force exerted by the bat if the ball is in contact with the bat for 0,13 s.
The question explicitly gives
the ball's mass,
the ball's initial velocity,
the ball's final velocity, and
the time of contact between bat and ball
We are asked to calculate the impulse
Since we do not have the force exerted by the bat on the ball (F
), we have to calculate the impulse from the change in momentum of the ball. Now, since
we need the ball's mass, initial velocity and final velocity, which we are given.
Firstly let us change units for the mass
Next we change units for the velocity
Similarly, 36 km
hr
= 10 m
s
.
Let us choose the direction from the batsman to the bowler as the positive direction. Then the initial velocity of the ball is
= -15 m
s
, while the final velocity of the ball is
= 10 m
s
.
Now we calculate the change in momentum,
Finally since impulse is just the change in momentum of the ball,
We are given
and we have calculated the impulse of the ball.
Which one of the following is NOT a unit of impulse?
A toy car of mass 1 kg moves eastwards with a speed of 2 m
s
. It collides head-on with a toy train. The train has a mass of 2 kg and is moving at a speed of 1,5 m
s
westwards. The car rebounds (bounces back) at 3,4 m
s
and the train rebounds at 1,2 m
s
.
Calculate the change in momentum for each toy.
Determine the impulse for each toy.
Determine the duration of the collision if the magnitude of the force exerted by each toy is 8 N.
A bullet of mass 20 g strikes a target at 300 m
s
and exits at 200 m
s
. The tip of the bullet takes 0,0001s to pass through the target. Determine:
the change of momentum of the bullet.
the impulse of the bullet.
the magnitude of the force experienced by the bullet.
A bullet of mass 20 g strikes a target at 300 m
s
. Determine under which circumstances the bullet experiences the greatest change in momentum, and hence impulse:
When the bullet exits the target at 200 m
s
.
When the bullet stops in the target.
When the bullet rebounds at 200 m
s
.
A ball with a mass of 200 g strikes a wall at right angles at a velocity of 12 m
s
and rebounds at a velocity of 9 m
s
.
Calculate the change in the momentum of the ball.
What is the impulse of the wall on the ball?
Calculate the magnitude of the force exerted by the wall on the ball if the collision takes 0,02s.
If the ball in the previous problem is replaced with a piece of clay of 200 g which is thrown against the wall with the same velocity, but then sticks to the wall, calculate:
The impulse of the clay on the wall.
The force exerted by the clay on the wall if it is in contact with the wall for 0,5 s before it comes to rest.