A 65.0 kg student is standing atop a spring in an elevator as it accelerates upward at 3.85 m/s2. The spring constant is 3000 N/m. By how much (in m) is the spring compressed, assuming that the local acceleration due to gravity is 9.80 m/s2?

Well, let's break it down, shall we? The student's mass is 65.0 kg. That's quite a hefty student! But we won't judge.

Now, the elevator is accelerating upwards at 3.85 m/s^2. That's some speedy elevator! Hang on tight!

The spring constant is 3000 N/m. It sounds like this spring means business.

To find out how much the spring is compressed, we need to compare the gravitational force acting on the student to the force created by the spring. Phew, math time!

The gravitational force acting on the student is given by the equation F_gravity = m * g, where m is the mass and g is the acceleration due to gravity (9.80 m/s^2).

So, the force of gravity on the student is F_gravity = 65.0 kg * 9.80 m/s^2. I'll leave you to calculate that.

Now, the force created by the spring is given by the equation F_spring = k * x, where k is the spring constant and x is the displacement or compression of the spring.

To find out how much the spring is compressed, we need to know the force created by the spring. We can equate the force of gravity to the force created by the spring. That gives us the equation F_gravity = F_spring.

Now, we can set the equations equal to each other: m * g = k * x. Rearranging to solve for x, we get x = m * g / k.

Now, you take over, calculator genius! Plug in the values we have and solve for x. The answer should be the amount the spring is compressed in meters. Good luck!

To find the compression of the spring, we need to calculate the gravitational force and the force exerted by the spring.

Step 1: Calculate the gravitational force:
The gravitational force (Fg) can be calculated using the formula:
Fg = mass * acceleration due to gravity

Given:
Mass (m) = 65.0 kg
Acceleration due to gravity (g) = 9.80 m/s^2

Substituting the values:
Fg = 65.0 kg * 9.80 m/s^2
Fg = 637.0 N

Step 2: Calculate the net force:
The net force (Fnet) on the student is equal to the difference between the force exerted by the spring (Fs) and the gravitational force (Fg).
Fnet = Fs - Fg

Step 3: Calculate the force exerted by the spring:
The force exerted by the spring (Fs) can be calculated using Hooke's Law which states that the force exerted by a spring is directly proportional to its compression or elongation.
Fs = spring constant * displacement

Given:
Spring constant (k) = 3000 N/m

Using Hooke's Law:
Fs = 3000 N/m * displacement

Since the spring is compressed in this case, the displacement will be negative.

Step 4: Calculate the net force:
Fnet = Fs - Fg
Fnet = 3000 N/m * displacement - 637.0 N

Since the elevator is accelerating upward, the net force equals the mass times acceleration:
Fnet = mass * acceleration

Given:
Acceleration (a) = 3.85 m/s^2

Substituting the values:
Fnet = 65.0 kg * 3.85 m/s^2
Fnet = 250.25 N

Step 5: Set up the equation and solve for displacement:
250.25 N = 3000 N/m * displacement - 637.0 N

Rearranging the equation:
3000 N/m * displacement = 250.25 N + 637.0 N
3000 N/m * displacement = 887.25 N

Dividing both sides by 3000 N/m:
displacement = 887.25 N / 3000 N/m
displacement ≈ 0.296 m

Therefore, the spring is compressed by approximately 0.296 m.

To find the compression of the spring, we need to consider the forces acting on the student and use Hooke's Law.

Let's break down the problem:

1. Calculate the force due to gravity acting on the student.
The force due to gravity is given by F_gravity = m * g, where m is the mass of the student and g is the acceleration due to gravity.
F_gravity = (65.0 kg) * (9.80 m/s^2) = 637.5 N.

2. Calculate the net force acting on the student.
The net force is the vector sum of the force due to gravity and the force due to the acceleration of the elevator.
F_net = F_gravity + F_elevator.
F_elevator = m * a, where a is the acceleration of the elevator.
F_elevator = (65.0 kg) * (3.85 m/s^2) = 250.25 N.
F_net = 637.5 N + 250.25 N = 887.75 N.

3. Apply Hooke's Law to find the spring compression.
Hooke's Law states that the force exerted by a spring is directly proportional to its displacement. The formula is F_spring = k * x, where k is the spring constant and x is the displacement.
Rearranging the formula, x = F_spring / k.
In this case, the force exerted by the spring (F_spring) is equal to the net force acting on the student.
x = F_net / k = 887.75 N / 3000 N/m = 0.2959 m.

Hence, the spring is compressed by approximately 0.296 m.