Peoples Physics Concepts

7.1. Momentum http://www.ck12.org

Example 2

John and Bob are standing at rest in middle of a frozen lake so there is no friction between their feet and the ice.

Both of them want to get to shore so they simultaneously push off each other in opposite directions. If John’s mass

is 50 kg and Bob’s mass is 40 kg and John moving at 5 m/s after pushing off Bob, how fast is Bob moving?

Solution

For this problem, we will apply conservation of momentum to the whole system that includes both John and Bob.
Since both of them are at rest to start, we know that the total momentum of the whole system must always be zero.
Therefore, we know that the sum of John’s and Bob’s momentum after they push off each other is also zero. We can
use this to solve for Bob’s velocity.

0 =mjvj+mbvb

−mbvb=mjvj

vb=−

mjvj

mb

vb=−

50 kg∗5 m/s

40 kg

vb=− 6 .25 m/s

The answer is negative because Bob is traveling in the opposite direction to John.

Watch this Explanation

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/397

Explore More

1. You find yourself in the middle of a frozen lake. There is no friction between your feet and the ice of the lake.
   You need to get home for dinner. Which strategy will work best?
   a. Press down harder with your shoes as you walk to shore.
   b. Take off your jacket. Then, throw it in the direction opposite to the shore.
   c. Wiggle your butt until you start to move in the direction of the shore.
   d. Call for help from the great Greek god Poseidon.


2. You and your sister are riding skateboards side by side at the same speed. You are holding one end of a rope
   and she is holding the other. Assume there is no friction between the wheels and the ground. If your sister lets
   go of the rope, how does your speed change?
   a. It stays the same.