physics - lesson 17_conservation of momentum problem - solving\ntotal momentum before = total momentum…

physics - lesson 17_conservation of momentum problem - solving\ntotal momentum before = total momentum after\n$p_{1\\ initial}+p_{2\\ initial}=p_{1\\ final}+p_{2\\ final}$\n(initial) $m_1v_1 + m_2v_2=m_1v_1 + m_2v_2$ (final)\n$m_1v_1 + m_2v_2=(m_1 + m_2)v_{final}$\n1. two suvs are traveling on the same road. suv a has a mass of 800 kg while suv b has a mass of 650 kg. suv a stops at a stop sign. suv b is traveling behind suv a with a momentum of 16250 kg m/s when it hits the back of suv a. after the collision, suv b has a momentum of 6500 kg m/s and suv a is forced forward. how much momentum is transferred from suv b in order to force suv a forward?\n2. a 4.0 - kg boy on a bike has an initial velocity of +10 m/s and collides with a 6.0 - kg girl that is stationary. after the collision, both children are stuck together. what is their final velocity?\n1. givens/want:\n2. equation:\n3. substitution:\n4. solve + units:

physics - lesson 17_conservation of momentum problem - solving\ntotal momentum before = total momentum after\n$p_{1\\ initial}+p_{2\\ initial}=p_{1\\ final}+p_{2\\ final}$\n(initial) $m_1v_1 + m_2v_2=m_1v_1 + m_2v_2$ (final)\n$m_1v_1 + m_2v_2=(m_1 + m_2)v_{final}$\n1. two suvs are traveling on the same road. suv a has a mass of 800 kg while suv b has a mass of 650 kg. suv a stops at a stop sign. suv b is traveling behind suv a with a momentum of 16250 kg m/s when it hits the back of suv a. after the collision, suv b has a momentum of 6500 kg m/s and suv a is forced forward. how much momentum is transferred from suv b in order to force suv a forward?\n2. a 4.0 - kg boy on a bike has an initial velocity of +10 m/s and collides with a 6.0 - kg girl that is stationary. after the collision, both children are stuck together. what is their final velocity?\n1. givens/want:\n2. equation:\n3. substitution:\n4. solve + units:

Answer

Explanation:

Step1: Identify the principle

Use conservation of momentum.

Step2: Solve for question 1

The momentum transferred from SUV B to SUV A is equal to the final - momentum of SUV A. So the momentum transferred is 6500 kg m/s.

Step3: Solve for question 2

  1. Givens/Want:
    • (m_1 = 4.0\ kg), (v_1=10\ m/s), (m_2 = 6.0\ kg), (v_2 = 0\ m/s), want (v_{final}).
  2. Equation:
    • According to the conservation of momentum (m_1v_1+m_2v_2=(m_1 + m_2)v_{final}).
  3. Substitution:
    • Substitute the values into the equation: ((4.0\ kg\times10\ m/s)+(6.0\ kg\times0\ m/s)=(4.0\ kg + 6.0\ kg)v_{final}), which simplifies to (40\ kg\cdot m/s=(10\ kg)v_{final}).
  4. Solve + Units:
    • Solve for (v_{final}): (v_{final}=\frac{40\ kg\cdot m/s}{10\ kg}=4\ m/s).

Answer:

  1. 6500 kg m/s
  2. 4 m/s