Spring constant

Classical Mechanics Level 3

Two springs are designed to absorb the kinetic energy of a 2000 kg 2000 \text{ kg} vehicle. If the maximum compressed length of the strings is to be 10 m 10 \text{ m} for a vehicle speed of 10 m/s, 10 \text{ m/s,} what is the spring constant required?

k = 2000 N/m k = 2000 \text{ N/m} k = 1000 N/m k = 1000 \text{ N/m} k = 500 N/m k = 500 \text{ N/m} k = 4000 N/m k = 4000 \text{ N/m}

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Srinivasa Satti by Srinivasa Satti

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1 solution

Nihar Mahajan
Oct 24, 2015

Assuming that the two springs do the same work , each spring will act on 1000 k g 1000 \ kg mass of the whole car. So we have the equation:

1 2 m v 2 = 1 2 k x 2 ⇒ 1000 × 10 × 10 = k × 10 × 10 ⇒ k = 1000 N / m \dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2 \\ \Rightarrow 1000\times 10\times 10=k\times 10\times 10 \\ \Rightarrow \boxed{k=1000 \ N/m}

  • m : Mass of the car on which one spring acts.

  • v : Velocity of vehicle

  • k : Spring constant

  • x : Compression of spring

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

A good, standard solution. It's a nice presentation decision to explain all your variable in the lookup table.

Challenge Taker Note: Nice, Standard Solution

Mehul Arora - 5 years, 4 months ago

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