Answer to Question #193654 in Classical Mechanics for Kaitlyn Hosking

Question

7.Police suspect that a van was breaking the speed limit when it collided with a parked car. Investigations provided them with the following data: mass of parked car                  = 800 kg,  mass of van = 1000 kg,  velocity of  car after collision = 5 m/s,  velocity of van after collision = 11 m/s

Show whether the van was breaking the 30 mph speed limit (equivalent to 13 m/s).

8.A dodgem car of mass 200 kg moves with a velocity of 3 m/s. The moving dodgem collides with a stationary one of mass 180 kg.

After the collision, the 200 kg dodgem continues to move in the same direction at a speed of 1 m/s.

Calculate the speed v with which the 180 kg (second) dodgem moves to the right after the collision.

Answer 1

$7.$

$\text{van: }$

$m_1 =1000 ;\vec u_1-?;\vec v_1= 11$

$\text{car:}$

$m_2 =800;\vec u_2=0;\vec v_2= 5$

$\vec u_1,\vec u_2\ \text{pre-collision speed}$

$\vec v_1, \vec v_2\ \text{speed after collision}$

$\text{according to the law of conservation of momentum:}$

$\vec p= m_1\vec u_1+m_2\vec u_2\ = m_1\vec u_1=1000\vec u_1$

$\vec p= m_1\vec v_1+m_2\vec v_2\ = 1000*11+800*5=15000$

$1000\vec u_1= 15000$

$\vec u_1= 15\frac{m}{s}>13\frac{m}{s}$

$\text{Answer: The van driver has exceeded the speed limit}$

$8.$

$\text{dodgem car first:}$

$m_1 =200 ;\vec u_1=3;\vec v_1= 1$

$\text{dodgem car second:}$

$m_2 =180 ;\vec u_2=0;\vec v_2-?$

$\vec u_1,\vec u_2\ \text{pre-collision speed}$

$\vec v_1, \vec v_2\ \text{speed after collision}$

$\text{according to the law of conservation of momentum:}$

$\vec p= m_1\vec u_1+m_2\vec u_2\ = 200*3=600$

$\vec p= m_1\vec v_1+m_2\vec v_2= 200*1+180\vec v_2$

$200*1+180\vec v_2 =600$

$\vec v_2=\frac{400}{180}\approx2.22\frac{m}{s}$

$\text{Answer: }\approx2.22\frac{m}{s}$