Question

A block of mass m=3.85 kg slides along a horizontal table with speed 0=8.00 m/s. At x=0, it hits a spring with spring constant =30.00 N/m, and it also begins to experience a friction force. The coefficient of friction is given by =0.200. How far has the spring compressed by the time the block first momentarily comes to rest?

Answer 1

To calculate the compression of the spring, first calculate the friction force using the coefficient of friction and normal force. Then, calculate the force exerted by the spring using Hooke's Law. Finally, equate the forces to find the compression of the spring.

Step-by-step explanation:

Given the mass of the block (m = 3.85 kg), the initial speed (v = 8.00 m/s), the spring constant (k = 30.00 N/m), and the coefficient of friction (μ = 0.200), we can calculate how far the spring compresses when the block first momentarily comes to rest.

First, we need to calculate the friction force acting on the block. The friction force can be determined using the equation:

Ffriction = μk × Fnormal

where μk is the coefficient of kinetic friction and Fnormal is the normal force.

Next, we can calculate the force exerted by the spring using Hooke's Law:

Fspring = -k × x

where k is the spring constant and x is the compression of the spring.

Finally, we can equate the forces acting on the block to find the compression of the spring:

Ffriction + Fspring = 0

By solving this equation, we can find the value of x, which represents the distance the spring has compressed.