In order to determine the normal force, we are going to need the angle of the hill, which we can calculate from the gravitational force that we are given. The vertical force of gravity is:

Its component in the direction of the sledder's movement is:

If you're wondering why sin was used, think about the situation practically. As the angle grows, the hill gets steeper, and there will be more gravitational force in the direction of acceleration. Sine is the function that gets larger as the angle gets larger.

No rearranging for the angle:

Plugging in the values from the problem statement:

Now we can use the FUN equation to determine the kinetic frictional force:

Now we need an expression for the normal force, which is the gravitational force multiplied by cosine:

Once again, if you're unsure why we used cosine, think about the situation practically. As the hill gets flatter (angle decreased), the normal force grows, and cos is the function that gets larger as the angle gets smaller. Now substituting this into the FUN equation, we get:

We have all of our values, so we can solve the problem:

Since the problem statement tells us that the sledder is traveling at a constant velocity, we know that the net force on the sledder is 0:

Now, we simply need to balance the 3 forces acting on the sledder: gravity, friction, and the tow rope. It's important to not that the force from the rope is up the hill, and the forces of gravity and friction are down the hill. In other words:

Beginning with the gravitational force, we have:

However, we need the component that is parallel with the sledder's motion:

If you're wondering why sine was used, think about the situation practically. As the angle grows, the hill gets steeper, and there will be more gravitational force in the direction of acceleration. Sin is the function that gets larger as the angle gets larger.

Now moving on to the frictional force. We will use the FUN equation:

We need an expression for the normal force, which is a component of the gravitational force:

Once again, if you're unsure why we used cosine, think about the situation practically. As the hill gets flatter (angle decreased), the normal force grows, and cos is the function that gets larger as the angle gets smaller. Now substituting this into the FUN equation, we get:

Substituting our expanding forces back into equation (1):

We have all of these values, so time to finish the problem:

By definition, , always points opposite of the objects direction of motion.  If the object is not moving, but an applied force  is attempted to move the object along a particular direction,  points opposite of the intended direction.

Use the following experience:

All energy will be kinetic, and final energy will be zero as the car has stopped.

Using the definition of the force of friction. (Frictional force points in the direction opposite of travel, so will be a negative value)

Solving for

Plugging in values

Frictional force is independent of surface area, it only depends on the normal force and the coefficient of friction.

Right when the box starts to slide, the magnitude of the frictional force is equal to the magnitude of the centripetal force.

Using the definition of frictional force.

Solving for

Plugging in values:

Solving for :

Plugging in values:

By constructing a force diagram, it can be seen that:

Right when the box starts to move, these will be equal

Solving for

Plugging in values:

Because the mass of object 1 is given, the force acting on it must be found in order to figure out how fast it is accelerating. These 3 variables are related by the equation:

There are 2 forces acting on mass 1. The first force is the tension in the rope. This tension is equal to the magnitude of the gravitational force created by object 2. This can be found using the equation:

where g is the gravity constant which is equal to . 

The other force acting on the object is friction. The force of friction can be found by multiplying the normal force exerted by the object on the surface that it is resting on by the coefficient of friction. This is demonstrated by the equation:

Where  is the coefficient of friction and N is the normal force. Static friction is the force of friction acting on an object that is not moving. because the magnitude of the force of static friction would not be as great as the magnitude of the force of tension in the rope the object would be moving. Because the object is moving, kinetic friction would be the other force that is acting on mass 1. Kinetic friction represents the friction exerted on an object that is moving on a surface. 

Because there are 2 forces acting on this object, a free body diagram can be made to illustrate these forces. 

T represents tension in the rope while F represents friction. The total net force can be found by subtracting the force of friction from the magnitude of tension in the rope. 

Acceleration of mass 1 can now be figured out because the force acting on the object has been found and the mass is given.

In order for mass 1 to remain stationary while mass 2 is experiencing free fall, the magnitude of the force of static friction acting on mass 1 must be greater than the magnitude of the force of tension in the rope that is created by mass 2. The force of tension in the rope is equal to the gravitational force that is created by mass 2. This force can be found using the equation:

The minimum coefficient of static friction would create a force in the opposite direction that has the same magnitude as the force found above. Force of static friction is equal to the coefficient static friction between an object and surface multiplied by the normal force exerted by the object being analyzed. This is represented by the following equation:

Where  is the coefficient of static friction and N is normal force. Normal force in this problem would be equal to the mass of object 1 multiplied by the gravity constant. By setting the 2 equations above equal to each other, minimum coefficient of static friction can be found. 

After plugging in given values,