Question

Momentum and collisions

Formula for Oomph
An important physical quantity, the name of which we’ll give later, corresponds to the intuitive idea of oomph. The more oomph something has, the harder it is to stop, and the more ability it has to knock other things over. Let’s figure out the formula for oomph .

A small pebble and a larger rock are thrown at the same speed.
Which one has more oomph? Why?

The rock is twice as massive as the pebble. Intuitively, how does the rock’s oomph compare to the pebble’s oomph? Is it twice as big? Half as big? Three times as big?

Picture two identical bowling balls, one of which is rolling faster than the other.
Which ball, the faster or slower one, has more oomph? Why?

The faster ball is exactly 7 times as fast as the slower one. Intuitively, how does the faster ball’s oomph compare to the slower ball’s oomph?

The physics concept corresponding to oomph is momentum. Building on your above answers, figure out a formula for momentum (oomph) in terms of mass and velocity. Explain how the formula expresses your intuitions from parts A and B above.

C. 1 kg cart collides with a 3 kg cart and, the 3 kg cart gets knock forward by the 1 kg cart, which comes to rest after the collision.
1. Using intuitions, guess the post-collision speed of the 3 kg cart.

2. According to the intuitive guess you just made, is the overall momentum of the two-cart system after the collision greater than, less than, or equal to the overall momentum before the collision?

3. Based on your work above, state a general rule about how the total momentum of a system changes during a collision.

Answer 1

1)The larger rock has more oomph as it has more mass.

2) Twice as big

3) The faster ball will have mpre oomph because it is having more speed.

4)the faster ball will have 7 times more oomph.

5) momentum should be directly proportional to mass of the object and its velocity. p=k* m*v.

Thus doubling mass will double the momentum and making the velocity 7 times will make momentum 7 times.

p1=k*m*v p2 = k*(2m)*v = 2 *k*m*v =2p1

p1=k*m*v p2 = k*(m)*(7v )= 7*k*m*v =7p1

3') the speed of the 3kg cart after collision will be one third of the speed of the 1kg cart before collision

Overall momentum of the two cart system shall remain constant

Total momentum of a system remains unchanged during collision