Question

The ice rink is very crowded, and there are a lot of inexperienced people learning to ice skate there. Tara is originally skating at 4.5 m/s and collides with Sarah who is at rest. After the collision, they hang on to each other in an effort to not fall over. They are no longer watching where they are going and end up running into Millicent who was just standing there. Then they all hang on to each other to avoid falling over. They fall over after 1.5 seconds. How far did the three girls travel before falling over? Assume that all three girls have a mass of about 55 kg.

A high school physics teacher is looking for fun new ways to get his students excited about learning momentum. He decides to try the somewhat dangerous demonstration of sticking a firecracker in an empty soda can and lighting it. After he lights the firecracker, the soda can and firecracker will travel very quickly in opposite directions. The mass of an empty soda can is 13.68 g (according to the first result from Google), and the mass of a small firecracker is 45 g. The teacher estimates that the firecracker should have a speed of 35 m/s. How fast should he expect the soda can to travel? Is this demonstration a good idea?

Answer 1

Solution:

We are given that a girl named Tara collides with another girl named Sarah in a skating rink and then both of them start moving together and collides with third person Millicent.

Three of them then move as single unit and finally fall.

We have to calculate the distance the three girls have travelled before falling.

The data given is:

Mass of each girl (m) =55 kg

Initial velocity of Tara (v_T) = 4.5 m/s

Initial velocity of Sarah (v_S) = 0 m/s

Initial velocity of Millicent (v_M) = 0 m/s

Time taken by three girls to fall (t) = 3 s

Now let's start with the solution-

By law of conservation of momentum, initial momentum=final momentum

or, total momentum before collision = total momentum after collison

First considering the case of Tara and Sarah,

Momentum before collision = mv_T + mv_S = (55*4.5) + 0 = 247.5 kg m/s

Momentum after collision = (m+m)v_TS     ( where v_TS is the combined speed of Tara and Sarah after collision)

247.5 = (55+55) v_TS ( Because value of final momentum= initial momentum)

247.5 = 110 v_TS

v_Ts= 247.5 / 110 = 2.25 m/s

Now, after this collision, Tara and Sarah will act as one person and Millicent will act as second person.

Again using the law of conservation of momentum:

Momentum before collision = (m+m) v_TS + mv_M = (55+55) * 2.25 + 0 ( because v_M = 0)

= 110*2.25 = 247.5 kg m/s

Momentum after collision = (m+m+m) v_TSM (where v_TSM is the combined speed of all three girls)

247.5 = (55+55+55) v_TSM    ( again because of law of conservation of momentum)

247.5 = 165 * v_TSM

v_TSM = 247.5 / 165 = 1.5 m/s

This is the combined velocity of all three girls after collision.

Now, let's say, the distance travelled by girls before falling is 'd' and time taken 't' = 1.5 sec

d= v_TSM *t

d= 1.5 * 1.5 = 2.25 m

The girls have travelled 2.25 m distance before falling apart.