A girl coasts down a hill on a sled, reaching

level ground at the bottom with a speed of
7.0 m/s. The coefficient of kinetic friction
between the sled’s runners and the hard, icy
snow is 0.054, and the girl and sled together
weigh 749 N.
The acceleration of gravity is 9.81 m/s
2
.
How far does the sled travel on the level
ground before coming to a rest?

To find out how far the sled travels on the level ground before coming to a rest, we can use the equations of motion.

The first step is to calculate the net force acting on the sled. The only force working against the sled's motion on the level ground is the force of kinetic friction. The formula for the force of kinetic friction is given by:

F_friction = coefficient of kinetic friction * normal force

Where the normal force is the force exerted on the sled due to its weight, and it is equal to the weight of the sled. So, in this case, the force of kinetic friction can be calculated as follows:

F_friction = 0.054 * 749 N

Next, we can calculate the acceleration of the sled using Newton’s second law of motion:

F_net = mass * acceleration

In this case, the sled and the girl have a combined weight of 749 N, and we can convert it to mass using the formula:

weight = mass * acceleration due to gravity

So, the mass of the sled and the girl can be calculated as follows:

749 N = mass * 9.81 m/s^2

Now, we can calculate the acceleration:

acceleration = F_net / mass

With the acceleration known, we can use the equation of motion:

v^2 = u^2 + 2*a*s

Where v is the final velocity (0 m/s since the sled comes to rest), u is the initial velocity (7.0 m/s), a is the acceleration, and s is the distance traveled.

Plugging in the values, we get:

0^2 = (7.0 m/s)^2 + 2 * acceleration * s

Since we know the initial velocity, final velocity, and acceleration, we can solve for the distance traveled (s). Rearranging the equation, we get:

s = (0^2 - (7.0 m/s)^2) / (2 * acceleration)

Plugging in the values and solving for s will give us the distance traveled by the sled on the level ground before coming to a rest.