Question

momentum problems

1. a 370 kg car is traveling at 38 m/s. what is its momentum?
2. a skateboarder with a momentum of 255 kg*m/s is traveling at 8 m/s. what is her mass?
3. what is the speed of a 3 kg bowling ball that has a momentum of 57 kg*m/s?

conservation of momentum problems

1. a 5,000 kg train engine moving at 20 m/s strikes a 450 kg car. how fast will the car fly away?
2. a 320 kg car thats traveling at 25 m/s strikes another car. the two cars stick together and have a combined mass of 915 kg. what velocity are the two cars now traveling at?
3. in a game of billiards, you hit the cue ball at a velocity of 32 m/s. all of the other pool balls it hits fly away at 4 m/s. what was the total mass of all of the pool balls that you broke up?

Explanation:

Step1: Recall the formula for momentum

The formula for momentum \(p\) is \(p = mv\), where \(m\) is mass and \(v\) is velocity.
For problem 24: Given \(m = 370\space kg\) and \(v=38\space m/s\), substitute into the formula \(p = mv\).
\(p=(370)(38)\)

Step2: Calculate the value

\(370\times38=(300 + 70)\times38=300\times38+70\times38=11400+2660 = 14060\space kg\cdot m/s\)

For problem 25: Given \(p = 255\space kg\cdot m/s\) and \(v = 8\space m/s\), use the formula \(p=mv\) and solve for \(m\). Rearranging gives \(m=\frac{p}{v}\)
\(m=\frac{255}{8}=31.875\space kg\)

For problem 26: Given \(p = 57\space kg\cdot m/s\) and \(m = 3\space kg\), use \(p = mv\) and solve for \(v\). Rearranging gives \(v=\frac{p}{m}\)
\(v=\frac{57}{3}=19\space m/s\)

For problem 27: Assuming elastic collision and conservation of momentum \(m_1v_1=m_2v_2\) (assuming train engine stops after collision, \(m_1 = 5000\space kg\), \(v_1=20\space m/s\), \(m_2 = 450\space kg\))
\(v_2=\frac{m_1v_1}{m_2}=\frac{5000\times20}{450}=\frac{100000}{450}\approx222.22\space m/s\)

For problem 28: Using conservation of momentum \(m_1v_1=(m_1 + m_2)v\) (where \(m_1 = 320\space kg\), \(v_1 = 25\space m/s\), \(m_1 + m_2=915\space kg\))
\(v=\frac{m_1v_1}{m_1 + m_2}=\frac{320\times25}{915}=\frac{8000}{915}\approx8.74\space m/s\)

Answer:

1. \(14060\space kg\cdot m/s\)
2. \(31.875\space kg\)
3. \(19\space m/s\)
4. \(\approx222.22\space m/s\)
5. \(\approx8.74\space m/s\)