Center of Mass, Impulse, Momentum, and Collisions

Question

You are driving a truck of mass 5 650 kg at 13 m/s. You accidentally hit a parked car. The car and the passengers have a total mass of 984 kg. (a) What is the speed of the car and the truck after the impact assuming that they are locked together? (b) If the impact lasts for 0.5 s, what force is experienced by an 80 kg passenger? Use GUESS METHOD

Answer 1

GUESS = Given, Unknown, Equations, Set-Up, Solve

Using the guess method, define your givens, unknowns (what you want to solve), equations, set-up (solve equations without values), solve (plug-in values).

a) This is an inelastic collision problem. You will need the following equation:

1. Given: You are given the mass (m) and velocity (v) of a moving truck. The parked car is not currently moving so your velocity is zero (v = 0). You can generate the left side of the above equation with this given. The two vehicles will stick together (inelastic collision). Knowing that the vehicles stick together gives you the right side of your equation (sum of masses times the final velocity).
2. Unknown: Final velocity
3. Equation: Use information from Given to create equation.
4. Set-up: Use algebra to rearrange equation and solve for your unknown.
5. Solve: Plug in your values and find your unknown.

b) Make sure to use GUESS method to solve part b.

1. Given: You now know your velocity from a. You also know the mass of the passenger. You'll want to assume that the vehicle is accelerating over the 0.5s timeframe given in the problem.
2. Unknown: Force (newtons)
3. Equations:
4. F = ma
5. a (acceleration) = Change in Velocity / time
6. Change in Velocity = Remember that the passenger is starting from a standstill and accelerating to the solved velocity from question a.
7. Set-up: Solve your equations above to find your force. Remember that you are only interested in the force experience by the passenger; therefore, you should carefully consider the mass value you use in your equation.
8. Solve: Plug in your values and solve for the unknown.