A 2kg mass is loaded into a spring cannon. The cannon\'s spring has a constant k

Question

A 2kg mass is loaded into a spring cannon. The cannon's spring has a constant k = 4000 abd the spring is compressed 0.8m. The mass is initially at rest. The flat surface is entirely made of a substance with a coefficient of kinetic friction mu(sub-k) = 0.6. All energy in the spring is converted to kinetic energy. There is no friction in the cannon.

Question 1: Before the mass is released, what is the potential energy of the spring?

Question 2: What is the kinetic energy of the mass the moment after release?

Question 3: What is the initial velocity of the mass?

Question 4: How far does it move before it comes to a stop?

Explanation / Answer

1)

Potential energy = 0.5*kx^2 = 0.5*4000*0.8^2 = 1280 J

2)

K.E after release = P.E = 1280 J <------By conservation of energy

3)

K.E = 0.5*mv^2

So, v = sqrt(2*K.E/m)

initial velocity = sqrt(2*(E)/m) = sqrt(2*1280/2) = 35.8 m/s <-----------answer

4)

As all the K.E is converted to work done by friction,

So, K.E = umg*x <------ u = coefficient of friction, x = distance moved before coming to rest

So, x = K.E/umg = 1280/(0.6*2*9.8) = 108.8 m <-------------answer

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