Energy & Momentum Problems (CP)

Mixed

Rule of Thumb: If the mass of the object stays the same it is

a conservation of Energy problem. If the mass of the object changes, it is a

conservation of momentum problem (inelastic collision)

If two objects bounce, it is a conservation of momentum problem (elastic collision)

If there is a spring, it is an energy problem

Example: A block with a mass of 25 kg starts from rest 6.0 m above the ground and slides down a frictionless ramp. What is the velocity of the block at the bottom of the ramp?

21(25 )(9.8)(6.0 ) (25 )

2kg m kg v

21

2mgy mv

Ei = Ef

Mass stays the same

V = 10.84 m/s

Draw the picture:

Example: At the bottom of the ramp, the 25 kg block collides inelasticly with 10. kg toy car at rest. What is the final velocity of the car-block combo?

pi = pf

Mass changes

(25 )(10.84 / ) 0 (25 10. ) fkg m s kg kg v

Vf =7.7 m/s

Draw the picture:

V=10.84 m/s

Example: 2:a) A 65 kg Olympic ice skater is coasting at 5.0 m/s on a frozen pond when his little brother (of mass 35 kg) falls from a tree and lands in his arms. Now how fast is the skater moving while still holding his brother? (ignore any velocity from his little brother)

pip

f

(65kg)(5.0m / s)0(65kg35kg)vf

vf3.25m / s 3.3m / s

b) The sudden appearance of his brother makes the skater hit a small stone and fall over. The friction between his jeans and the ice bring him, still holding his brother, to a stop in 1.5 m. What is the force of friction between his jeans and the ice?

KEiW

f

1

2mv

i

2 Ffd

12(6535)(3.25)2 F

f1.5

NNFf 350352

Example: 2

A 0.25 kg Nerf arrow is fired from spring-loaded gun at a 10.0 kg target sitting on a frozen (frictionless) pond. After impact, the arrow and target slide across the pond at 3.7 m/s. What is the spring constant of the Nerf gun if the spring was compressed 30.0 cm when the arrow was fired? (assume the arrow does not fall during flight) (Yes, I know this is a little unrealistic)

K = 64,000 N/m