To test the resiliency of its bumper during low-speed collisions, a 4 750-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 6.00 106 N/m and compresses 3.82 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

Lillie Odom

Physics

12 December, 22:32

To test the resiliency of its bumper during low-speed collisions, a 4 750-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 6.00 106 N/m and compresses 3.82 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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Derrick Melendez · Answer 1

1.4 m/s

Explanation:

m = mass of the automobile = 4750 kg

k = spring constant of the bumper = 6 x 10⁶ N/m

v = speed of the car just before the impact

x = compression of the bumper = 3.82 cm = 0.0382 m

using conservation of energy

Spring potential energy = Kinetic energy of the car

(0.5) k x² = (0.5) m v²

k x² = m v²

(6 x 10⁶) (0.0382) ² = (4750) v²

v = 1.4 m/s