Since the car is stopped at the end, 

Combining equations:

Solving for 

From this, it can be seen that doubling the coefficient of friction would cut the stopping distance in half.

Work is due to friction:

Solving for 

Plugging in values:

Work is due to friction:

Solving for 

Plugging in values:

Because the block is traveling on an inclined ramp and experiences friction, the two main forces at work here are a component of gravitational force and kinetic frictional force.

 The total force acting on the block can be written as , where  is the component of gravitational force in the direction of motion, and  is the kinetic frictional force.

We know that forces can be expressed as , and kinetic friction can be expressed as . Hence our total force can be expressed as . The normal force can be further expressed as 

The component of gravity parallel to the ramp is given by , while the component of gravity perpendicular to the ramp is given by .

Our total force can hence be expressed as .

Thus, 

and 

Solving for the coefficient of friction:

We can use the expression for conservation of energy to solve this problem:

The problem statement tells us that the sledder is initially at rest, so we can eliminate initial kinetic energy. Also, if we assume that the bottom of the hill has a height of 0, we can eliminate final potential energy to get:

  (1)

From here we need to determine what is going to contribute to work. The only extra piece of information we have in this problem is that there is an average frictional force. Therefore that will be the only source of work. Let's began expanding each term, going from left to right:

  (2)

Note that we didn't mark the height as an initial height because we assumed that the bottom of the hill has a height of 0.

Where d is the length of the hill. We can calculate this distance using the height and angle of the hill.

Rearranging for distance:

Substituting this back into our expression for work, we get:

  (3)

Now our final term:

    (4)

Now substituting expression 2, 3, and 4 into expression 1, we get:

The reason we are subtracting friction is because it is removing energy from the system. Another way we could have written our initial expression would be to have work on the final state and then friction would be positive.

Rearranging for the frictional force:

We have all of these values, so time to plug and chug:

You simply need to know the formula for the potential energy stored in a spring to solve this problem. The formula is:

where k is the spring constant, and x is the distance from equilibrium

We can rearrange this to get:

Plugging in our values, we get:

Since the block is motionless, we know that our forces will cancel out:

There are three forces in play: one from each spring, as well as the force of gravity. If we assume that forces pointing up are positive, we can write:

Plugging in expressions for each spring force, we get:

Rearring for the displacement of the top spring, we get:

Since the block is motionless, we can assume that the forces cancel out:

If we designate any forces pointing downward as positive, we can write:

Inserting expressions for each force, we get:

Rearranging for mass, we get:

There are two ways to solve this problem: the first involves calculating the spring constant and the second does not. We'll go through both methods.

Calculating Spring Constant

We can use the expression for the force of a spring:

At equilibrium, the force of the spring equals the force of gravity:

Rearranging for the spring constant and plugging in values, we get:

Now, apply this equation when the spring is on a different planet:

Rearranging for displacement and plugging in values, we get:

Without Calculating Spring Constant

We can write the force equation for each scenario. Let the subscript 1 denote Earth, and 2 denote the other planet:

Using these equations, we can set up a proportion:

Rearranging for the displacement of scenario 2 and plugging in values: