A block is sliding along a frictionless surface at a speed of 3.6 m/s. It hits a spring of spring stiffness constant k = 150 N/m. How far has the spring compressed when the block comes to a stop?

To find out how far the spring has compressed when the block comes to a stop, we can use the principle of conservation of mechanical energy.

The initial kinetic energy of the block is equal to the potential energy stored in the compressed spring when the block comes to a stop.

The initial kinetic energy (KE) of the block can be calculated using the formula:
KE = 0.5 * m * v^2

where m is the mass of the block and v is its velocity.

Given that the speed of the block is 3.6 m/s, and assuming no other given information, we need to know the mass of the block to calculate its initial kinetic energy.

Once we have the initial kinetic energy, we can use it to calculate the potential energy stored in the spring when the block comes to a stop.

The potential energy (PE) stored in the spring can be calculated using the formula:
PE = 0.5 * k * x^2

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

Since the question gives us the value of the spring stiffness constant k (150 N/m), we can use it to find the compression distance x.

Setting the initial kinetic energy equal to the potential energy, we have:
0.5 * m * v^2 = 0.5 * k * x^2

We can rearrange this equation to solve for x:
x = √[(m * v^2) / k]

Given that we need the mass of the block to calculate x, it seems to be missing from the question. Without the mass of the block, we cannot proceed further to calculate the compression distance of the spring.