1.A kitten sits in a lightweight basket near theedge of a table. A person accidentally knocksthe basket off the table. As the kitten and basketfall, the kitten rolls, turns, kicks, and catches thebasket in its claws. The basket lands on the floorwith the kitten safely inside. If air resistanceis negligible, what is the acceleration of thekitten-basket system while the kitten and basketare in midair?
(A) The acceleration is directed downward withmagnitude less than g because the basket is light.
(B) The acceleration is directed downward with magnitude equal to g because the system is a projectile.
(C) The acceleration fluctuates because of the rolling, turning, and kicking motion of the kitten.
(D) The acceleration cannot be determined without knowing how hard the basket is pushed.
2.A solid metal bar is at rest on a horizontalfrictionless surface. It is free to rotate abouta vertical axis at the left end. The figures belowshow forces of different magnitudes that areexerted on the bar at different locations. In whichcase does the bar’s angular speed about the axisincrease at the fastest rate?
3. To analyze the characteristics and performance of the brakes on a 1500 kg car, researchers collected the data shown in the table above. It shows the car’s speed when the brakes are first applied and the corresponding braking distance required to stop the car. The magnitude of the average braking force on the car is most nearly
(A) 75,000 N
(B) 30,000 N
(C) 12,000 N
(D) 1600 N
4. Mars moves in an elliptical orbit around the Sun, and the mass of Mars is much less than the mass of the Sun. At the instant shown above, Mars is getting farther away from the Sun. How does this affect the potential energy of the Mars-Sun system and the magnitude of Mars’s angular momentum with respect to the Sun?
5. An ice-skater is moving at a constant velocity across an icy pond. The skater throws a snowball directly ahead. Which of the following correctly describes the velocity of the center of mass of the skater-snowball system immediately after the snowball is thrown? Assume friction and air resistance are negligible.
(A) It is equal to the velocity of the snowball.
(B) It is equal to the new velocity of the skater.
(C) It is equal to half the original velocity of the skater.
(D) It is equal to the original velocity of the skater.
1. (7 points, suggested time 13 minutes)
Two blocks A and B of equal mass m are on a frictionless track, as shown in the figure above. Block A, initially moving with speed v1, has a perfectly elastic collision with block B. Block B has a speed v1 immediately after the collision, and then it travels around a circular loop of radius R, where R is much larger than the size of the blocks. The speed of block B at the top of the loop is vtop. Block B then slides up a ramp until it comes momentarily to rest at a height h above the floor.
(a) Derive an equation for the height h in terms of m, R,vtop, and g, as appropriate.
(b) Suppose that the speed v1 of block A is doubled. Will the final height of block B be greater than, less than,or equal to 2h?
____Greater than 2h ____Less than 2h ____Equal to 2h
(c) Blocks A and B (both of mass m) are moved to a different frictionless track, as shown above. Let vA be the minimum initial speed for block A that allows block B to make it over the hump in the track. Block A is then replaced with a larger block, block C, which has mass 2m, as shown below.
Block C makes a completely inelastic collision with block B so that both blocks stick together and travel along the track. What is the minimum initial speed vC that block C must have so that the two-block system makes it over the hump? Express your answer in terms of vA