Solving Spring Problems Involving Mass and Frictionless Floor

[Naeem]

A block of mass m = 4.5 kg rests on a frictionless floor. It is attached to a spring with a relaxed length L = 3 m. The spring has spring constant k = 16 N/m and is relaxed when hanging in the vertical position. The block is pulled d = 3 m to one side. In this problem, the block is always constrained to move on the floor (i.e. it never leaves the floor).


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a) By what amount is the spring extended?
DL = m *


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b) What is the potential energy stored in the spring?
Uspring = J *
12.3 OK


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c) The block is released but is constrained to move horizontally on the frictionless floor. What is the maximum speed it attains?
|v|max= m/s *
2.34 OK


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Let's change the problem a bit. When the spring is vertical (hence, unstretched), the block is given an initial speed equal to 1.8 times the speed found in part (c).
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d) How far from the initial point does the block go along the floor before stopping?
Dmax = m *
4.287 OK


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e) What is the magnitude of the acceleration of the block at this point (when the spring is stretched farthest)?
|a| = m/s2
0.638 NO

HELP: What is the force exerted by the spring on the block when the spring is fully stretched?

I am not able to figure out part e. I'm stuck

here is what I did F = ma = k * delta L

Plugged in m , k and delta L

found a to be 8.25 m/s2, which is wrong, anybody tell me what is wrong?

 

[thermodynamicaldude]

The force a spring exerts on an object is F = -kx.

 

[Astronuc]

If the spring is vertical in its relaxed mode, and the block is move laterally, then the spring forms the hypotenuse of an isosceles right triangle with two sides of 3 m.

Here I am assuming the floor is horizontal with the normal parallel to the axis of the spring.

 

[Naeem]

Can anybody help me with part e) here please.

Thanks,