A block of mass 11.2 kg slides from rest down a frictionless 24.0° incline and is stopped by a strong spring with a spring constant 31.3 kN/m (note the unit). The block slides 8.90 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest momentarily, how far has the spring been compressed? Answer in units of cm and use 9.8 m/s2 for g.

I can't really figure out how to start to try to solve this problem. Help please?

Fb = m*g = 11.2kg * 9.8N/kg = 109.8 N. =

Force of block.

Fp = 109.8*sin24 = 44.64 N. = Force parallel to the incline.

d = (1m/31,300N) * Fp
d = (1m/31,300N) * 44.64N = 0.0014262 m.
= 0.143 cm.

To solve this problem, we can use the principles of conservation of energy. The potential energy gained by the block as it slides down the incline will be equal to the potential energy stored in the compressed spring.

Let's start by finding the potential energy gained by the block as it slides down the incline:

1. Calculate the height of the incline:
To calculate the height, we can use the formula:
height = (length of incline) * sin(angle)
height = 8.90 m * sin(24.0°)

2. Calculate the potential energy gained by the block:
The potential energy gained is given by the formula:
potential energy = mass * gravity * height
potential energy = 11.2 kg * 9.8 m/s² * (height calculated in step 1)

Now, let's find the potential energy stored in the spring when the block is stopped:

3. Calculate the potential energy stored in the spring:
The potential energy stored in a spring is given by the formula:
potential energy = (1/2) * spring constant * (compression distance)^2
We need to find the compression distance. Let's call it 'd'.
From the problem statement, the block comes to rest momentarily against the spring.
Therefore, the potential energy stored in the spring will be equal to the potential energy gained by the block.
(1/2) * 31.3 kN/m * (d in cm)^2 = potential energy calculated in step 2

Now, we can solve for 'd', which represents the compression distance:

4. Rearrange the equation from step 3 to solve for 'd':
(d in cm)^2 = (2 * potential energy calculated in step 2) / (31.3 kN/m)
d in cm = sqrt((2 * potential energy calculated in step 2) / (31.3 kN/m))

Plug in the values and calculate the compression distance:

5. Substitute the values into the equation from step 4 and solve for 'd':
d in cm = sqrt((2 * potential energy calculated in step 2) / (31.3 kN/m))

By following these steps, you should be able to calculate the compression distance of the spring in centimeters.