How much kinetic energy is lost in the collision

Question

Assignment:

Question 1. A boy on a 2.4 kg skateboard initially at rest tosses a(n) 7.9 kg jug of water in the forward direction.

If the jug has a speed of 3.2 m/s relative to the ground and the boy and skateboard move in the opposite direction at 0.62 m/s, find the boy's mass.

Question 2. A 90.0 kg astronaut is working on the engines of a spaceship that is drifting through space with a constant velocity. The astronaut turns away to look at Earth and several seconds later is 40.3 m behind the ship, at rest relative to the spaceship. The only way to return to the ship without a thruster is to throw a wrench directly away from the ship. The wrench has a mass of 0.492 kg, and the astronaut throws the wrench with a speed of 21.9 m/s.

How long does it take the astronaut to reach the ship?

Question 3. A student performs a ballistic pendulum experiment using an apparatus similar to that shown in the figure.

Initially the bullet is fired at the block while the block is at rest (at its lowest swing point).

After the bullet hits the block, the block rises to its highest position, see dashed block in the figure, and continues swinging back and forth.

The following data is obtained:

the maximum height the pendulum rises is 2 cm, at the maximum height the pendulum subtends an angle of 29.9 ? , the mass of the bullet is 84 g, and the mass of the pendulum bob is 814 g.

The acceleration of gravity is 9.8 m/s 2.

Determine the initial speed of the bullet.

Question 4. Gayle runs at 4.97 m/s and dives on a sled, initially at rest onto the top of a frictionless snow covered hill. After she and the sled have descended a vertical distance of 6.12 m, her brother who is initially at rest hops on her back and together they continue down the hill.

The acceleration of gravity is 9.8 m/s 2 .

What is their speed at the bottom if the total vertical drop is 19.1 m? Gayle's mass is 63.2 kg, the sled's is 2.74 kg and her brother's is 24.2 kg.

Question 5. A 1370 kg car skidding due north on a level frictionless icy road at 294 km/h collides with a 2397.5 kg car skidding due east at 200 km/h in such a way that the two cars stick together.

At what angle (-180? ≤ θ ≤ +180? ) East of North do the two coupled cars skid off at?

Question 6. How much kinetic energy is lost in the collision?

Question 7. Assume an elastic collision (ignoring friction and rotational motion).

A queue ball initially moving at 3.4 m/s strikes a stationary eight ball of the same size and mass. After the collision, the queue ball's final speed is 0.88 m/s.

Find the queue ball's angle θ with respect to its original line of motion.

Question 8. A water molecule consists of an oxygen atom with two hydrogen atoms bound to it.

The angle between the two bonds is 106?

If each bond is 0.117 nm long, how far from the oxygen atom is the center of mass of the molecule? Take the mass of an oxygen atom to be 16 times the mass of a hydrogen atom.

Question 9. A rectangular metal plate has uniform density and thickness. A circular hole is cut out of the plate as shown on the figure:

Calculate the x coordinate of the remaining plate's center of mass.

Note: by reasons of symmetry, the y coordinate of the center of mass is zero.

Question 10. A rocket is fired vertically upward. At the instant it reaches speed of 263 m/s, it explodes into three fragments with equal masses. Immediately after the exposion, the first fragment flies vertically with speed 508 m/s, while the second fragment flies horizontally with speed 387 m/s.

What is the speed of the third fragment immediately after the exposion?

Question 11. Romeo entertains Juliet by playing his guitar from the rear of their boat in still water.

After the serenade, Juliet carefully moves to the rear of the boat to plant a kiss on Romeo's cheek.

The 128 kg boat is facing the shore and Romeo is at the far end of the boat (aware from the shore). The 42.2 kg Juliet initially a distance 3.31 m from her lover, moves all the way to the end of the boat to plant the kiss on the 94.1 kg Romeo. How far does the boat move toward shore?

Question 12. The surfaces are frictionless. The tracks are 60? from horizontal.

A 522 kg mass is released from rest on a track at a height 4.4 m above a horizontal surface at the foot of the slope. It collides elastically with a 585 kg mass initially at rest on the horizontal surface, as shown in the figure. The mass 585 kg slides up a similar track.

The acceleration of gravity is 9.8 m/s²

What is the speed of the block 585 kg immediately after the collision?

Question 13. To what maximum height h2 above the horizontal surface will the mass 585 kg slide?

Question 14. A 3460 kg rocket has 3620 kg of fuel on board. The rocket is coasting through space at 137 m/s and needs to boost its speed to 344 m/s. It does this by firing its engines and ejecting fuel at a relative speed of 847 m/s until the desired speed is reached.

How much fuel is left on board after this maneuver?

Question 15. A jet aircraft is traveling at 300 m/s in horizontal flight. The engine takes in air at a rate of 61.4 kg/s and burns fuel at a rate of 3.68 kg/s. The exhaust gases are ejected at 734 m/s relative to the aircraft.

Find the thrust of the jet engine.

Question 16. Find the delivered power.