A 56kg student is standing atop a spring in an elevator that is accelerating upward at 3.1m/s2 . The spring constant is 2100N/m .

By how much is the spring compressed?

To determine how much the spring is compressed, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

First, let's calculate the weight of the student. The weight can be calculated using the formula:

Weight = mass × acceleration due to gravity

Weight = 56 kg × 9.8 m/s^2 (acceleration due to gravity)

Weight = 548.8 N

Next, we need to calculate the net force acting on the student. The net force is the difference between the force exerted by the spring and the weight of the student. The force exerted by the spring can be determined using Hooke's Law:

Force = spring constant × displacement

The displacement of the spring is the amount by which it is compressed. Let's assume it is x meters.

Force = 2100 N/m × x

Now, the net force can be calculated:

Net Force = Force exerted by the spring - Weight

We can set up an equation to find the displacement (x) of the spring:

2100 N/m × x - 548.8 N = 0

Solving this equation will give us the displacement of the spring, which represents the amount it is compressed.

x = 548.8 N / 2100 N/m

x = 0.2619 m (rounded to four decimal places)

Therefore, the spring is compressed by approximately 0.2619 meters.