(a) To find the velocity of the sled and person as they move away, we can use the principle of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision:
m1 * v1 + m2 * v2 = (m1 + m2) * vf
where m1 and v1 are the mass and velocity of the person, m2 and v2 are the mass and velocity of the sled, and vf is the final velocity of the combined person and sled.
Since the sled is initially at rest, v2 = 0, and the equation simplifies to:
m1 * v1 = (m1 + m2) * vf
Now we can plug in the given values and solve for vf:
(58.4 kg) * (+3.84 m/s) = (58.4 kg + 10.7 kg) * vf
vf = (58.4 kg * 3.84 m/s) / (58.4 kg + 10.7 kg) = 224.256 / 69.1 = 3.244 m/s
So the velocity of the sled and person as they move away is +3.244 m/s, with the positive sign indicating that they move in the same direction as the person was initially running.
(b) To find the coefficient of kinetic friction between the sled and the snow, we can apply Newton's second law:
f_friction = μ * f_norm
where f_friction is the frictional force, μ is the coefficient of kinetic friction, and f_norm is the normal force acting on the sled and person. Since there is no vertical acceleration, the normal force equals the combined weight of the person and sled:
f_norm = (m1 + m2) * g = 69.1 kg * 9.81 m/s^2 = 677.031 N
The work-energy principle states that the work done by friction (W_friction) must equal the change in kinetic energy:
W_friction = μ * f_norm * d
where d is the distance traveled before coming to rest (31.5 m). The change in kinetic energy is given by:
ΔKE = 0.5 * (m1 + m2) * vf^2 - 0.5 * (m1 + m2) * 0^2
Since vf = 3.244 m/s:
ΔKE = 0.5 * 69.1 kg * (3.244 m/s)^2 = 365.438 J
Now we can set up an equation using the work-energy principle:
μ * f_norm * d = ΔKE
μ * 677.031 N * 31.5 m = 365.438 J
μ = 365.438 J / (677.031 N * 31.5 m) = 0.0166
So the coefficient of kinetic friction between the sled and the snow is 0.0166.
A 58.4-kg person, running horizontally with a velocity of +3.84 m/s, jumps onto a 10.7-kg sled that is initially at rest.
(a) Ignoring the effects of friction during the collision, find the velocity of the sled and person as they move away. (Indicate the direction with the sign of your answer.)(b) The sled and person coast 31.5 m on level snow before coming to rest. What is the coefficient of kinetic friction between the sled and the snow?
1 answer