<< Chapter < Page | Chapter >> Page > |
In the collision pictured in [link] , two carts collide inelastically. Cart 1 (denoted carries a spring which is initially compressed. During the collision, the spring releases its potential energy and converts it to internal kinetic energy. The mass of cart 1 and the spring is 0.350 kg, and the cart and the spring together have an initial velocity of . Cart 2 (denoted in [link] ) has a mass of 0.500 kg and an initial velocity of . After the collision, cart 1 is observed to recoil with a velocity of . (a) What is the final velocity of cart 2? (b) How much energy was released by the spring (assuming all of it was converted into internal kinetic energy)?
Strategy
We can use conservation of momentum to find the final velocity of cart 2, because (the track is frictionless and the force of the spring is internal). Once this velocity is determined, we can compare the internal kinetic energy before and after the collision to see how much energy was released by the spring.
Solution for (a)
As before, the equation for conservation of momentum in a two-object system is
The only unknown in this equation is . Solving for and substituting known values into the previous equation yields
Solution for (b)
The internal kinetic energy before the collision is
After the collision, the internal kinetic energy is
The change in internal kinetic energy is thus
Discussion
The final velocity of cart 2 is large and positive, meaning that it is moving to the right after the collision. The internal kinetic energy in this collision increases by 5.46 J. That energy was released by the spring.
What is an inelastic collision? What is a perfectly inelastic collision?
Mixed-pair ice skaters performing in a show are standing motionless at arms length just before starting a routine. They reach out, clasp hands, and pull themselves together by only using their arms. Assuming there is no friction between the blades of their skates and the ice, what is their velocity after their bodies meet?
A small pickup truck that has a camper shell slowly coasts toward a red light with negligible friction. Two dogs in the back of the truck are moving and making various inelastic collisions with each other and the walls. What is the effect of the dogs on the motion of the center of mass of the system (truck plus entire load)? What is their effect on the motion of the truck?
Notification Switch
Would you like to follow the 'Introduction to applied math and physics' conversation and receive update notifications?