Impulse And Momentum
a. A 0.14 kg baseball is hit by a bat. State 1 is just before being hit. State 2 is just
after being hit. What is the impulse that the bat put on the ball to make this
b. A 0.45 kg soccer ball has been kicked. State 1 is immediately after being kicked.
State 2 is the highest point on the trajectory. What is the impulse that gravity
put on the ball between State 1 and State 2?
State 1 State 2
!” = 40& + 30) [m/s] !* = −10& − 2) [m/s]
!” = 18 ‘ + 20 + [m/s]
2. Conservation of Momentum
a. Cart C has a mass of 20kg and can roll freely in the x-direction. Bag A and Bag B
each have a mass of 10kg. The bags are thrown onto the cart. They do not slide
or bounce off the cart. The velocities of the bags and cart, just before the bags
land, are shown on the drawing. What is the speed of the combined cart and
bags just after the bags land on the cart?
b. A 20 kg dog is standing on a stationary 15 kg sled on smooth ice (State 1). The dog
jumps off the back of the sled. Immediately after jumping, the dog’s velocity is 3
m/s directed 25° above the horizontal (State 2). The sled does not tip while the
dog jumps. What is the velocity of the sled immediately after the dog jumped?
!” = 1 m/s
!% = 3 m/s
Velocities just before
impact are shown
!⃗( = 3) − 3, [m/s]
!” = 0
STATE 2 !!!
!+& = 3 ./0
Conservation of Energy and/or Conservation of Momentum
3. Two packages are tossed onto a sled, which is on an icy surface. The
packages do not bounce or slide off of the sled. The sled can only move in
the horizontal (x) direction. After impact the sled slides for some distance
and then stops due to friction.
a. The velocities of the packages just before impact are shown on the
figure. What is the velocity of the combined sled and packages
immediately after impact?
b. The kinetic friction coefficient between the sled and the ice is 0.05
How far will the combined sled and packages slide before coming to
Just before impact
Just after impact
$% = ?
Sled comes to rest
)* = 0.05
Δ. = ?
$/0 = 4 2/4
$50 = 0
$70 = 3 2/4 27 = 15 :;
2/ = 10 :;
25 = 5 :;
4. Ball A rotates without friction on the end of a 30cm rod. Cart B rolls freely
in the horizontal direction. Initially Cart B is a rest, and Ball A is released
from rest with the rod horizontal. When the ball gets to the bottom of its
swing, it impacts Cart B. After impact the Ball rebounds to 30°. What is the
speed of Cart B just after impact, �'( = ?
As usual in this part of the course, neglect the size of the ball and the mass
of the rod.
Hint: This problem is not as complicated as it might first appear. I made
four drawings to help split it into events that need conservation of energy
versus conservation of momentum. Be careful of the sign of �+, and use
correct value for gravity whether leaving it in cm-gram-sec system or
changing to m-kg-sec system.
A B B
State 1 State 2
State 3 State 4
Ball A released from rest Just before impact
Just After Impact speed of Ball A is zero
%&) = 0 %&’ = 0
*+, = ?
*/1 = 2 !
34 = 200 6
3& = 600 6
8 = 30 93