Particle dropped on platform with spring - Compression of springs

[rasa]

A massless platform is kept on a light elastic spring.
When a particle of mass 100g is dropped on the platform from a hieght of 24cm it strikes the platform and compresses the spring by 1cm.
From what hieght should the particle be dropped to cause a compression of 4cm?
[text book answer: 396cm]

 

[radou]

Use the fact that energy (kinetic + potential) is conserved.

 

[kyle8921]

Based on the given information, we can use the equation for potential energy to solve for the initial height of the particle. The potential energy at the point of release is equal to the potential energy at the point of impact (assuming no energy is lost to other factors such as air resistance). We can set up the equation as follows:

mgh = kx

Where m is the mass of the particle (0.100 kg), g is the acceleration due to gravity (9.8 m/s^2), h is the initial height, k is the spring constant, and x is the compression distance (0.04 m).

Solving for h, we get:

h = (kx)/mg

Since the spring constant and the mass of the particle are given, we can plug in the values and solve for h:

h = [(2.5 N/m)(0.04 m)]/(0.100 kg)(9.8 m/s^2)

h = 0.102 m

Therefore, the particle should be dropped from a height of 102 cm (or 1.02 m) to cause a compression of 4 cm. This is equivalent to 396 cm as given in the textbook answer.