To test the resiliency of its bumper during low-speed collisions, a 3 690-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 8.00 106 N/m and compresses 3.86 cm as the car is brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed or transferred away during impact with the wall?

Question

Skyler Bauer

Physics

17 February, 18:32

To test the resiliency of its bumper during low-speed collisions, a 3 690-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 8.00 106 N/m and compresses 3.86 cm as the car is brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed or transferred away during impact with the wall?

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Muhammad Norton · Answer 1

1.8 m/s

Explanation:

m = mass of the automobile = 3690 kg

k = force constant of the spring = 8 x 10⁶ N/m

x = compression of the spring = 3.86 cm = 0.0386 m

v = speed of the car before impact

Using conservation of energy

Kinetic energy of automobile before impact = Spring potential energy of bumpers

(0.5) m v² = (0.5) k x²

(3690) v² = (8 x 10⁶) (0.0386) ²

v = 1.8 m/s