a) The frictional force on the back sled can be found using Newton's second law. The net force acting on the back sled is the tension in the rope connecting the sleds minus the frictional force. So we have:
Net force = Tension - Frictional force
Since the sleds are accelerating, the net force is equal to the mass of the back sled times its acceleration. Rearranging the equation, we get:
Frictional force = Tension - (mass of back sled * acceleration)
Plugging in the given values, we get:
Frictional force = Tension - (55.0 kg * 1.02 m/s^2)
b) The tension in the rope connecting the sleds can be found by considering the forces acting on the front sled. The only horizontal force acting on the front sled is the tension in the rope, and this force must be equal to the product of the mass of the front sled and its acceleration. So we have:
Tension = mass of front sled * acceleration
Plugging in the given values, we get:
Tension = 60.0 kg * 1.02 m/s^2
c) To find how far the sleds will travel after the student lets them go, we need to consider their initial velocity. Since the student starts from rest and runs for 3.00 s, the velocity of the sleds when he lets them go is equal to the magnitude of the force he applied divided by the sum of the masses of his friends:
Velocity = force / (mass of back friend + mass of front friend)
Plugging in the given values, we get:
Velocity = 230 N / (55.0 kg + 60.0 kg)
Once we have the initial velocity, we can find the distance traveled using the equation:
Distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Plugging in the given values, we get:
Distance = (velocity * 3.00 s) + (1/2 * 1.02 m/s^2 * (3.00 s)^2)
A student has tied together two sleds with a rope. Two of his friends, with masses of 55.0 kg and 60.0 kg, are riding in the sleds, one in each (55.0 kg in the back, 60.0 kg in front). Th e student uses another rope to pull the sleds with a horizontal force of magnitude 230 N. Th e sleds accelerate with a magnitude of 1.02 m/ s 2 . Th e front sled experiences a force of friction of magnitude 58.8 N. Assume that the masses of the sleds are negligible . a) What is the frictional force on the back sled? b) What is the tension in the rope connecting the sleds? c) Th e student pulling the sleds starts from rest, runs fo r 3.00 s, and then lets the sleds go. How far will the sleds travel after he lets them go?
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