2. A 2300 kg truck moving at 12 m/s collides with a stationary 1200 kg passenger car, and the two stick together. Assuming that they are free to move afterward, what is the momentum of the truck+car object after the collision?
a) 7.9 kg m/s
b) 14000 kg m/s
c) 42000 kg m/s
d) 9500 kg m/s
e) 28000 kg m/s
3. 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 9.9 m/s, what was the velocity of ball B before the collision?
a) -5.0 m/s
b) 0.0 m/s
c) 5.0 m/s
d) 20 m/s
e) -9.9 m/s
4. A 1100 kg car sliding on frictionless ice at 13 m/s hits a stationary 2400 kg minivan. The two vehicles are locked together after impact on the ice. What is their speed after impact?
a) 6.0 m/s
b) 0.0 m/s
c) 4.1 m/s
d) 8.9 m/s
e) 13 m/s
5. A 4.0 kg ball of clay traveling at 10 m/s collides with a 20 kg ball of clay traveling in the same direction at 2.0 m/s. What is their combined speed if the two balls stick together when they touch?
a) 80 m/s
b) 24 m/s
c) 2.0 m/s
d) 3.3 m/s
e) 1.0 m/s
2. Momentum is conserved in a collision. The momentum before the collision is given by the sum of the individual momenta of the truck and car, and after the collision, it is given by the momentum of the combined truck+car object.
Before the collision:
Momentum of truck = mass of truck * velocity of truck = 2300 kg * 12 m/s = 27600 kg m/s
Momentum of car = mass of car * velocity of car = 1200 kg * 0 m/s (stationary) = 0 kg m/s
After the collision:
Momentum of truck+car = (mass of truck + mass of car) * velocity of truck+car
Since the truck and car stick together, their combined mass is given by the sum of their individual masses:
Mass of truck+car = mass of truck + mass of car = 2300 kg + 1200 kg = 3500 kg
Now, we can calculate the velocity of the truck+car object after the collision:
Momentum of truck+car = 3500 kg * velocity of truck+car
Setting the initial momentum equal to the final momentum (due to conservation of momentum):
27600 kg m/s + 0 kg m/s = 3500 kg * velocity of truck+car
Solving for velocity of truck+car:
velocity of truck+car = (27600 kg m/s + 0 kg m/s) / 3500 kg
velocity of truck+car = 7.9 m/s
The momentum of the truck+car object after the collision is 7.9 kg m/s. Therefore, the correct answer is option a) 7.9 kg m/s.
3. Before the collision, the momentum of ball A is given by the product of its mass and velocity:
Momentum of A = mass of ball A * velocity of ball A = 5.0 kg * 9.9 m/s = 49.5 kg m/s
Since the two balls stick together after the collision and are at rest, the total momentum after the collision is 0 kg m/s.
By conservation of momentum, the initial momentum must be equal to the final momentum:
49.5 kg m/s + momentum of ball B = 0 kg m/s
Since the velocity of ball B before the collision is opposite in direction to that of ball A, we can say that the momentum of ball B is negative:
-momentum of ball B = 49.5 kg m/s
Dividing both sides of the equation by the mass of ball B:
momentum of ball B = -49.5 kg m/s / (2 * mass of ball A)
Since the mass of ball A is given as 5.0 kg, the mass of ball B is 2 * 5.0 kg = 10.0 kg:
momentum of ball B = -49.5 kg m/s / (2 * 5.0 kg)
momentum of ball B = -4.95 m/s
Therefore, the velocity of ball B before the collision is -4.95 m/s. The correct answer is option e) -9.9 m/s (closest to -4.95 m/s).
4. Momentum is conserved in a collision. The momentum before the collision is given by the sum of the individual momenta of the car and minivan, and after the collision, it is given by the momentum of the combined car+minivan object.
Before the collision:
Momentum of car = mass of car * velocity of car = 1100 kg * 13 m/s = 14300 kg m/s
Momentum of minivan = mass of minivan * velocity of minivan = 2400 kg * 0 m/s (stationary) = 0 kg m/s
After the collision:
Momentum of car+minivan = (mass of car + mass of minivan) * velocity of car+minivan
Since the car and minivan stick together, their combined mass is given by the sum of their individual masses:
Mass of car+minivan = mass of car + mass of minivan = 1100 kg + 2400 kg = 3500 kg
Now, we can calculate the velocity of the car+minivan object after the collision:
Momentum of car+minivan = 3500 kg * velocity of car+minivan
Setting the initial momentum equal to the final momentum (due to conservation of momentum):
14300 kg m/s + 0 kg m/s = 3500 kg * velocity of car+minivan
Solving for velocity of car+minivan:
velocity of car+minivan = (14300 kg m/s + 0 kg m/s) / 3500 kg
velocity of car+minivan = 4.1 m/s
Therefore, the speed of the car+minivan object after the collision is 4.1 m/s. The correct answer is option c) 4.1 m/s.
5. Since the two balls stick together when they touch, the mass and velocity of the combined balls after the collision can be calculated using the conservation of momentum.
Before the collision:
Momentum of ball A = mass of ball A * velocity of ball A = 4.0 kg * 10 m/s = 40 kg m/s
Momentum of ball B = mass of ball B * velocity of ball B = 20 kg * 2.0 m/s = 40 kg m/s
After the collision:
Momentum of combined balls = (mass of ball A + mass of ball B) * velocity of combined balls
Since the two balls stick together, their combined mass is given by the sum of their individual masses:
Mass of combined balls = mass of ball A + mass of ball B = 4.0 kg + 20 kg = 24 kg
Now, we can calculate the velocity of the combined balls after the collision:
Momentum of combined balls = 24 kg * velocity of combined balls
Setting the initial momentum equal to the final momentum (due to conservation of momentum):
40 kg m/s + 40 kg m/s = 24 kg * velocity of combined balls
Solving for velocity of combined balls:
velocity of combined balls = (40 kg m/s + 40 kg m/s) / 24 kg
velocity of combined balls = 3.3 m/s
Therefore, the combined speed of the two balls after the collision is 3.3 m/s. The correct answer is option d) 3.3 m/s.