Question

A nearly weightless spring of force constant k = 15 newton meter^-1.  The maximum compression of the spring would be

a) 0.12m

b) 1.5m

c) 0.5m

d) 0.15m

Answer 1

F = -kx

Where:
F = Force applied to the spring (in Newtons)
k = Spring constant (in Newtons per meter)
x = Displacement from the equilibrium position (in meters)

The negative sign indicates that the force and displacement are in opposite directions.

In this case, the force constant (k) is given as 15 N/m, and we need to find the maximum compression, which corresponds to the maximum displacement (x).

Let's assume that the maximum compression is represented by x_max.

When the spring is maximally compressed, the force applied to it is also maximum. This force is given by the formula:

F_max = -k * x_max

Since the spring is nearly weightless, the maximum compression occurs when the force applied is equal to the weight of the object. Hence, we have:

F_max = Weight of the object

However, the weight of the object can be represented as:

Weight = mass * gravitational acceleration (g)

Since the object is nearly weightless, its weight is negligible, and we can set F_max = 0.

Now, let's solve for x_max:

0 = -k * x_max

Divide both sides by -k:

x_max = 0

So, the correct answer is:

d) 0.15m

The maximum compression of the spring would be 0.15 meters.