On a frozen pond, a 13.2 kg sled is given a kick that imparts to it an initial speed of v0 = 2.48 m/s. The coefficient of kinetic friction between sled and ice is μk = 0.123. Use the work kinetic energy theorem to find the distance the sled moves before coming to rest.
initial KE= forcefriction*distance
1/2 m vi^2=mg*mu*distance
solve for distance.
To find the distance the sled moves before coming to rest, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to its change in kinetic energy.
In this case, the work done on the sled is equal to the kinetic friction force multiplied by the distance traveled. This work is done to decrease the kinetic energy of the sled until it comes to rest.
The kinetic friction force can be calculated using the equation:
Fk = μk * N
where Fk is the kinetic friction force and N is the normal force. The normal force is equal to the weight of the sled, which can be calculated as:
N = m * g
where m is the mass of the sled and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the values given in the problem, we have:
N = (13.2 kg) * (9.8 m/s^2) = 129.36 N
Fk = (0.123) * (129.36 N) = 15.91 N (approximately)
The work done by the kinetic friction force is equal to the force multiplied by the displacement (distance traveled). Since the sled comes to rest, the work done is equal to the initial kinetic energy of the sled. The initial kinetic energy can be calculated using the equation:
KE = (1/2) * m * v0^2
Substituting the given values, we have:
KE = (1/2) * (13.2 kg) * (2.48 m/s)^2 = 40.96 J (approximately)
Therefore, the work done by the kinetic friction force is 40.96 J.
The work done by the kinetic friction force is also equal to the force multiplied by the distance traveled (d). Therefore, we can rearrange the equation to solve for d:
d = work / Fk
Substituting the values, we have:
d = 40.96 J / 15.91 N = 2.57 meters (approximately)
Thus, the sled moves a distance of approximately 2.57 meters before coming to rest.