What kind of collision is this? What formulas do I use for a and b?

Question

Bill forgets to put his car in park, and it starts rolling forward. When it is moving at a speed of 2 m/s, it collides with Tanya's car, which is moving 3 m/s backward. Bill's car bounces backward at a speed of 1.2 m/s, it collides with Tanya's, which is moving 3 m/s backward. Bill's car bounces backward at a speed of 1.2 m/s. Bill's car has a mass of 1100 kg and Tanya's car has a mass of 800 kg. 

 

a. What is the velocity of Tanya's car after the collision?

 

b. Assuming all lost kinetic energy is converted to heat, how much energy is converted to heat during the collision? 

Answer 1

This problem(a) will be solved by applying law of conservation of momentum. According to this law, when two bodied collide, momentum will always be conserved, ie. the sum of momentum of Bill's car and Tanya's car before collision and after collision will be same.

 

Before collision,

Velocity is a vector quantity so if we take Bill's car velocity direction(forward) positive then Tanya's car velocity direction(backward) will be negative as it is moving opposite to Bill's car. Momentum is also a vector quantity so we take Tanya's car momentum direction(backward) as negative. 

 

Bill's car momentum = m_b v_b = 1100x2=2200 kg.m/s (in forward direction)

 

Tanya's car momentum =m_t v_t= 800x (-3) = -2400 kg.m/s (in backward direction)

 

After collision, Lets Bill's car velocity is denoted as V_b Tanya's velocity after collision is V_t

Bill's car momentum= m_b  V_b= 1100 x( -1.2) = -1320 kg.m/s (in backward direction because car is moving backward after collison)

 

Tanya's car momentum = m_t V_t = 800xV_t

 

according to law of conservation of momentum,

 

m_b v_b + m_t v_t = m_b V_b  + m_t V_b 

put all the values in this equation,

 

2200 + (-2400) = -1320 + 800xV_t

 

-200 = -1320 + 800xV_t

 

V_t = 1.4 m/s

 

So after collision Tanya's car will move  with velocity of 1.4 m/s in forward direction.

 

 

b) Kinetic energy before and after collision will be conserved. 

 

So here,

 

kinetic energy = 1/2 m v² will be used to calculate the lose of energy. You just calculate the sum of kinetic energy of Bill's car and Tanya's car before collision an after collision. and then calculate loss of kinetic energy by subtracting the kinetic energy after collision from the kinetic energy before collision. 

 

KE before collision =  Bill's car kinetic energy+Tanya's car energy = 1/2 (1100)(2)² + 1/2 (800)(3)²= 6800 J

 

KE after collision = Bill's car kinetic energy+ Tanya's car energy = 1/2(1100)(1.2)² + 1/2 (800)(1.4)² = 1576 J

 

Loss in kinetic energy = KE before collision - KE after collision 

                                = (6800-1576) J

                                = 5224 J

 

If all lost kinetic energy is converted into heat then during collision 5224 J energy will be converted into heat.