Use the worked example above to help you solve this problem. In a crash test, a

Question

Use the worked example above to help you solve this problem. In a crash test, a car of mass 1.42 103 kg collides with a wall and rebounds as shown in the figure. The initial and final velocities of the car are vi = -15.1 m/s and vf = 2.72 m/s, respectively. If the collision lasts for 0.165 s, find (a) the impulse delivered to the car due to the collision and (b) the size of and direction ('+' or '-') of the average force exerted on the car.

Impulse: 25304 kg m/s
Average force: 153357.6 N

a) Use the values from PRACTICE IT to help you work this exercise. Suppose the car doesn't rebound off the wall, but the time interval of the collision remains at 0.165 s. In this case, the final velocity of the car is zero. Find the average force exerted on the car.

answer in N

Explanation / Answer

Mass of the car is m = 1.42*10^3 kg Initial speed is v_i = - 15.1 m/s final speed is v_f = 2.72 m/s Initial momentum is p_i = 1.42*10^3 kg * - 15.1 m/s                                         = - 2.144*10^4 kg m/s Final momentum is p_f = m v_f                                       = 1.42*10^3 kg * 2.72 m/s                                       = 0.386*10^3 kg m/s Impulse I = 0.386*10^3 kg m/s - ( - 2.144*10^4 kg m/s)                   = 2.53*10^4 kg m/s b) Average force exerted on the car is F_av = p / t                                                                     = 2.53*10^4 kg m/s / 0.165 s                                                                     = 1.533*10^5 N 2 ) Final momentum is zero    The averge force exerted on the car is F = - ( p) / t                                                                     = 0 - ( - 2.144*10^4 kg m/s / 0.165 s )                                                                      = + 1.299*10^5 N

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