Question

1. what happens to the speed of the wagon as the rain collects inside of it? a) it decreases b) it remains constant c) it increases 7. which takes more force to catch, a bowling ball or a ping pong ball? a) bowling ball because it has less momentum b) both require the same amount of force when catching c) ping pong ball because it has more momentum d) bowling ball because it has more momentum 8. a runner has a momentum of 670 kg m/s and is traveling at a velocity of 9 m/s. what is his mass? a) 80 kg b) 0.0134 kg c) 6030 kg d) 74.4 kg 9. if you double the velocity of an object, then its momentum will __________ a) will half b) will quadruple (x4) c) will be quartered (x 1/4) d) will double 10. the total momentum before a collision is __________ the total momentum after a collision. a) less than b) equal to c) more than d) it depends on the type of collision 11. which of the following has the least amount of momentum? a) an ant at rest b) an ant walking along the ground c) an elephant running d) an elephant walking 12. what is the unit for momentum? a) kg/sec b) kg m/sec c) m/sec d) kg/m 13. if 2 objects collide and stick together, what will happen to their velocities? a) velocities will stay the same b) none of the above c) velocities will decrease d) velocities will increase

Explanation:

Step1: Recall momentum - mass and velocity relationship

Momentum \(p = mv\), where \(m\) is mass and \(v\) is velocity.

Step2: Analyze question 6

As rain collects in the wagon, mass \(m\) increases. According to the law of conservation of momentum (\(p_{initial}=p_{final}\), \(m_1v_1=(m_1 + \Delta m)v_2\)), since \(p\) is constant and \(m\) increases, velocity \(v\) decreases. So the answer to question 6 is a).

Step3: Analyze question 7

Momentum \(p = mv\). A bowling - ball has a much larger mass than a ping - pong ball. Assuming similar velocities when catching, the bowling ball has more momentum. According to Newton's second law \(F=\Delta p/\Delta t\), more force is required to stop an object with more momentum. So the answer to question 7 is d).

Step4: Analyze question 8

Given \(p = mv\), we can solve for \(m\) when \(p = 670\ kg\cdot m/s\) and \(v = 9\ m/s\). Rearranging the formula gives \(m=\frac{p}{v}=\frac{670}{9}\approx74.4\ kg\). So the answer to question 8 is d).

Step5: Analyze question 9

Since \(p = mv\), if we double the velocity (\(v' = 2v\)), then \(p'=m\times(2v)=2mv = 2p\). So the momentum will double. The answer to question 9 is d).

Step6: Analyze question 10

According to the law of conservation of momentum, the total momentum before a collision is equal to the total momentum after a collision. The answer to question 10 is b).

Step7: Analyze question 11

An ant at rest has \(v = 0\), so its momentum \(p=mv = 0\) (since \(v = 0\)). An ant walking, an elephant running, and an elephant walking all have non - zero velocities and non - zero masses, so non - zero momenta. The answer to question 11 is a).

Step8: Analyze question 12

Since \(p = mv\), with \(m\) in kg and \(v\) in m/s, the unit of momentum is \(kg\cdot m/s\). So the answer to question 12 is b).

Step9: Analyze question 13

When two objects collide and stick together (in - elastic collision), according to the law of conservation of momentum \(m_1v_1+m_2v_2=(m_1 + m_2)v_{final}\). The combined mass \((m_1 + m_2)\) is larger than the individual masses, and since total momentum is conserved, the final velocity \(v_{final}\) is less than the initial velocities of the individual objects. So the velocities will decrease. The answer to question 13 is c).

Answer:

1. a) It decreases
2. d) bowling ball because it has more momentum
3. d) 74.4 kg
4. d) will double
5. b) equal to
6. a) An ant at rest
7. b) kg m/sec
8. c) velocities will decrease