A block of mass m = 2.5 kg rests on a frictionless floor. It is attached to a sp

Question

A block of mass m = 2.5 kg rests on a frictionless floor. It is attached to a spring with a relaxed length L = 6 m. The spring has spring constant k = 18 N/m and is relaxed when hanging in the vertical position. The block is pulled d = 4 m to one side. In this problem, the block is always constrained to move on the floor (i.e. it never leaves the floor).

a) By what amount is the spring extended?

b) What is the potential energy stored in the spring?

c) The block is released but is constrained to move horizontally on the frictionless floor. What is the maximum speed it attains?

Let's change the problem a bit. When the spring is vertical (hence, unstretched), the block is given an initial speed equal to 2 times the speed found in part (c).

d) How far from the initial point does the block go along the floor before stopping?

e) What is the magnitude of the acceleration of the block at this point (when the spring is stretched farthest)?

Explanation / Answer

the force acting on block is F = ma the force on spring is F1 = kx Here,F = F1 or ma = kx or a = kx/m where a is acceleration of block,k = 18 N/m,x = 4 m and m = 2.5 kg we know that v^2 - u^2 = 2ax where v = 0 and u is initial velocity of block or u = (2ax)^1/2 time taken by block to stop is v = u + at or t = u/a the distance travelled by block before stopping is S = ut + (1/2)at^2

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