# Mass on Spring

1. Nov 20, 2004

### 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?

2. Nov 20, 2004

### thermodynamicaldude

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

3. Nov 20, 2004

### Astronuc

Staff Emeritus
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.

4. May 11, 2005

### Naeem

Can anybody help me with part e) here plz.

Thanks,