1. Ball A has a mass of 5.0 kg. Ball B has twice the mass of ball A. The two balls collide and stick together in a perfectly inelastic collision. After the collision the combined balls are at rest. If the velocity of ball A before the collision was 11 m/s, what was the velocity of ball B before the collision?
a) -5.5 m/s
b) 0.0 m/s
c) 22 m/s
d) -11 m/s
e) 5.5 m/s
2. Which of the following equipment is the best choice for investigating elastic or nearly elastic collisions?
a) crash test cars with front ends that crumple upon impact to absorb all the initial kinetic energy
b) a ball of soft clay that flattens when it hits the ground
c) two sliding carts on a frictionless track that stick together after impact
d) marble launcher that causes two marbles to collide with each other
e) dropping a bowling ball from a balcony so that it makes a dent in the dirt below
3. A 1100 kg car sliding on frictionless ice at 16 m/s hits a stationary 2100 kg minivan. The two vehicles are locked together after impact on the ice. What is their speed after impact?
a) 8.4 m/s
b) 16 m/s
c) 11 m/s
d) 5.5 m/s
e) 0.0 m/s
4. A sphere of mass 6 kg is moving at 3 m/s to the right until it smacks into a second stationary sphere of mass 2 kg. After the collision, both spheres travel to the right: the first sphere at 1.50 m/s, and the second sphere at 4.50 m/s. What kind of collision took place?
a) This is an inelastic (but not perfectly inelastic) collision.
b) This situation is impossible.
c) More information is needed.
d) This is an elastic or nearly elastic collision.
e) This is a perfectly inelastic collision.
5. One sphere of mass 1 kg is moving at 5 m/s to the right until it collides with a stationary, 2 kg sphere. After the collision, both spheres travel to the right: the 1 kg sphere at 1 m/s, and the 2 kg sphere at 2 m/s. What kind of collision took place?
a) an inelastic (but not perfectly inelastic) collision
b) More information is needed.
c) This situation is impossible.
d) a perfectly inelastic collision
e) an elastic collision
1. To solve this problem, we can use the principle of conservation of momentum. Before the collision, the momentum of ball A is given by the product of its mass (5.0 kg) and velocity (11 m/s), which is (5.0 kg)(11 m/s) = 55 kg·m/s. Since the combined balls are at rest after the collision, the total momentum after the collision is zero. The momentum of ball B before the collision can be calculated using the equation:
(5.0 kg)(11 m/s) + (2(5.0 kg))(v) = 0
55 kg·m/s + 10 kg(v) = 0
10 kg(v) = -55 kg·m/s
v = -5.5 m/s
Therefore, the velocity of ball B before the collision was -5.5 m/s. Therefore, the answer is a) -5.5 m/s.
2. The best choice for investigating elastic or nearly elastic collisions is c) two sliding carts on a frictionless track that stick together after impact. This is because in an elastic collision, kinetic energy is conserved, which means the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Two sliding carts that stick together after impact will allow for the most accurate measurement and analysis of the velocities before and after the collision, as the kinetic energy can be directly calculated.
3. To solve this problem, we can use the principle of conservation of momentum. Before the collision, the total momentum is given by the sum of the momenta of the two vehicles. Since the minivan is stationary, its momentum is zero. Therefore, the total momentum before the collision is (1100 kg)(16 m/s) = 17600 kg·m/s. After the collision, the two vehicles are locked together and move with a common velocity. Let's call this velocity v. According to the principle of conservation of momentum, the total momentum after the collision is zero:
(1100 kg + 2100 kg)(v) = 0
3200 kg(v) = 0
v = 0.0 m/s
Therefore, the speed of the two vehicles after the collision is 0.0 m/s. Therefore, the answer is e) 0.0 m/s.
4. To determine the type of collision that took place, we can compare the total kinetic energy before and after the collision. Before the collision, the total kinetic energy is given by the sum of the kinetic energies of the two spheres. The first sphere has a mass of 6 kg and a velocity of 3 m/s, resulting in a kinetic energy of (1/2)(6 kg)(3 m/s)^2 = 27 J. The second sphere is stationary, so its kinetic energy is zero. Therefore, the total kinetic energy before the collision is 27 J + 0 J = 27 J. After the collision, the total kinetic energy is given by the sum of the kinetic energies of the two spheres. The first sphere has a mass of 6 kg and a velocity of 1.50 m/s, resulting in a kinetic energy of (1/2)(6 kg)(1.50 m/s)^2 = 6.75 J. The second sphere has a mass of 2 kg and a velocity of 4.50 m/s, resulting in a kinetic energy of (1/2)(2 kg)(4.50 m/s)^2 = 20.25 J. Therefore, the total kinetic energy after the collision is 6.75 J + 20.25 J = 27 J, which is equal to the total kinetic energy before the collision. This indicates that kinetic energy is conserved, so the collision is elastic or nearly elastic. Therefore, the answer is d) This is an elastic or nearly elastic collision.
5. To determine the type of collision that took place, we can compare the total kinetic energy before and after the collision. Before the collision, the total kinetic energy is given by the sum of the kinetic energies of the two spheres. The first sphere has a mass of 1 kg and a velocity of 5 m/s, resulting in a kinetic energy of (1/2)(1 kg)(5 m/s)^2 = 12.5 J. The second sphere is stationary, so its kinetic energy is zero. Therefore, the total kinetic energy before the collision is 12.5 J + 0 J = 12.5 J. After the collision, the total kinetic energy is given by the sum of the kinetic energies of the two spheres. The first sphere has a mass of 1 kg and a velocity of 1 m/s, resulting in a kinetic energy of (1/2)(1 kg)(1 m/s)^2 = 0.5 J. The second sphere has a mass of 2 kg and a velocity of 2 m/s, resulting in a kinetic energy of (1/2)(2 kg)(2 m/s)^2 = 4 J. Therefore, the total kinetic energy after the collision is 0.5 J + 4 J = 4.5 J, which is less than the total kinetic energy before the collision. This indicates that kinetic energy is not conserved, so the collision is inelastic (but not perfectly inelastic). Therefore, the answer is a) an inelastic (but not perfectly inelastic) collision.