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On the ceiling, a spring is attached with a  3 kg mass to the other end. Here on earth, the displacement is 0.15m. What would be the displacement of the spring on Mars if the planet has a gravitational acceleration of g= 3.71 m/s2

On the ceiling, a spring is attached with a  3 kg mass to the other end. Here on earth, the displacement is 0.15m. What would be the displacement of the spring on Mars if the planet has a gravitational acceleration of g= 3.71 m/s2

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On the ceiling, a spring is attached with a  3 kg mass to the other end. Here on earth, the displacement is 0.15m. What would be the displacement of the spring on Mars if the planet has a gravitational acceleration of g= 3.71 m/s2

Expert Solution
Step 1

Given:

  • The mass attached to the spring is m=3 kg.
  • The distance covered by mass on Earth is xe=0.15 m.
  • The acceleration due to gravity on Mars is g=3.71 m/s2.

The formula to calculate the gravitational force acting on mass on Earth is,

Fe=mge

Here, Fe is the gravitational force on Earth, m is the mass and ge is the acceleration due to gravity on Earth.

The formula to calculate the force acting on mass due to spring on Earth is,

Fs=kxe

Here, Fs is the force acting on mass due to spring, k is the force constant of spring and xe is the distance covered by mass on Earth.

When the system is in equilibrium, then both the forces are balanced which is given by,

Fe=Fs

Substitute the known values in the formula and solve to obtain the formula of force constant.

mge=kxek=mgexe

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