A girl coasts down a hill on a sled, reaching level ground at the bottom with a speed of 6.6 m/s. The coefficient of kinetic friction between the sled's runners and the hard, icy snow is 0.047, and the girl and sled together weigh 755 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?
Answer in units of m.
To find out how far the sled travels on the level ground before coming to a rest, we need to determine the deceleration of the sled first. The deceleration can be calculated using the equation:
a = μ * g,
where a is the deceleration, μ is the coefficient of kinetic friction, and g is the acceleration due to gravity.
Given that the coefficient of kinetic friction (μ) is 0.047 and the acceleration due to gravity (g) is 9.81 m/s^2, we can substitute these values into the equation to find the deceleration:
a = 0.047 * 9.81 = 0.46007 m/s^2.
Next, to determine the distance (d) the sled travels on the level ground before coming to a rest, we can use the kinematic equation:
v^2 = u^2 + 2as,
where v is the final velocity (0 m/s since the sled comes to rest), u is the initial velocity (6.6 m/s), a is the acceleration (0.46007 m/s^2), and s is the distance.
Substituting the values into the equation:
0 = (6.6)^2 + 2 * 0.46007 * s.
Simplifying the equation:
0 = 43.56 + 0.92014s.
Rearranging the equation:
0.92014s = -43.56.
Divide both sides by 0.92014 to solve for s:
s ≈ -47.354.
Since distance cannot be negative in this context, we can conclude that the sled travels approximately 47.354 meters on the level ground before coming to a rest.