A boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 6.9 m/s. If the coefficient of friction between the sled's runners and snow is 0.045 and the boy and sled together weigh 580 N, how far does the sled travel on the level surface before coming to rest?
To find the distance the sled travels on the level surface before coming to rest, we can use the concept of work and energy.
First, let's determine the initial kinetic energy of the sled when it reaches the level surface. The kinetic energy (KE) is given by the formula:
KE = 1/2 * m * v^2
where m is the mass of the boy and sled together, and v is the speed of the sled. Since weight (W) is equal to mass multiplied by acceleration due to gravity, we can relate the weight and mass:
W = m * g
where g is the acceleration due to gravity (9.8 m/s^2).
Therefore, the mass (m) can be calculated as:
m = W / g
Substituting the given weight (580 N) and the value of g (9.8 m/s^2) into the equation, we can find the mass:
m = 580 N / 9.8 m/s^2
Next, we can calculate the initial kinetic energy (KE) using the given speed (6.9 m/s) and the calculated mass:
KE = 1/2 * m * v^2
Finally, we can use the concept of work and energy to determine the distance (d) the sled travels before coming to rest. The work done by friction (Wfriction) can be calculated as:
Wfriction = -μ * m * g * d
where μ is the coefficient of friction, m is the mass, g is the acceleration due to gravity, and d is the distance.
The work done by friction is equal to the initial kinetic energy of the sled since the sled comes to rest:
Wfriction = KE
Therefore, by substituting the values, we can solve for the distance (d):
-μ * m * g * d = KE
d = KE / (-μ * m * g)
Substituting the values for KE, μ, m, and g, we can calculate the distance (d) the sled travels on the level surface before coming to rest.