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Molodets [167]
2 years ago
7

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 b

umper 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?
Physics
1 answer:
Mariana [72]2 years ago
8 0

Answer:

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

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A 225-g object is attached to a spring that has a force constant of 74.5 N/m. The object is pulled 6.25 cm to the right of equil
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1.137278672 m/s

+5.9 cm or -5.9 cm

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Maximum speed is given by

v_m=A\omega\\\Rightarrow v_m=A\sqrt{\dfrac{k}{m}}\\\Rightarrow v_m=6.25\times 10^{-2}\times \sqrt{\dfrac{74.5}{0.225}}\\\Rightarrow v_m=1.137278672\ m/s

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Velocity is at any instant is given by

\dfrac{v_m}{3}=\omega\sqrt{A^2-x^2}\\\Rightarrow \dfrac{A\omega}{3}=\omega\sqrt{A^2-x^2}\\\Rightarrow \dfrac{A}{3}=\sqrt{A^2-x^2}\\\Rightarrow \dfrac{A^2}{9}=A^2-x^2\\\Rightarrow A^2-\dfrac{A^2}{9}=x^2\\\Rightarrow x^2=\dfrac{8}{9}A^2\\\Rightarrow x=A\sqrt{\dfrac{8}{9}}\\\Rightarrow x=6.25\times 10^{-2}\sqrt{\dfrac{8}{9}}\\\Rightarrow x=\pm 0.0589255650989\ m

The locations are +5.9 cm or -5.9 cm

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2 years ago
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