two sleds that are tied together are pulled across an icy surface with an applied force of 200N [E]. the mass of sled 1 is 20.0kg and the mass of sled 2 is 14.0kg. the coefficient of kinetice friction for each sled is 0.30.
a) calculate the acceleration of the sleds
b) determine the magnitude of the tension in the rope between the sleds
To solve the problem, we can break it down into two parts: first, finding the net force acting on the sleds, and then using that information to find the acceleration and tension.
a) The net force acting on the sleds can be found by subtracting the force of friction from the applied force. The force of friction can be calculated using the equation F_friction = μ * F_normal, where μ is the coefficient of kinetic friction and F_normal is the normal force (equal to the weight of the sled).
For sled 1:
Weight of sled 1 = mass of sled 1 * gravitational acceleration
= 20.0 kg * 9.8 m/s^2
= 196 N
Force of friction on sled 1 = coefficient of kinetic friction * normal force on sled 1
= 0.30 * 196 N
= 58.8 N
For sled 2:
Weight of sled 2 = mass of sled 2 * gravitational acceleration
= 14.0 kg * 9.8 m/s^2
= 137.2 N
Force of friction on sled 2 = coefficient of kinetic friction * normal force on sled 2
= 0.30 * 137.2 N
= 41.16 N
Net force = applied force - force of friction
= 200 N - (58.8 N + 41.16 N)
= 100.04 N [E]
The net force is the force responsible for the acceleration of the sleds. To find the acceleration, we use the equation F = m * a, where F is the net force, m is the total mass of the sleds, and a is the acceleration.
Total mass of sleds = mass of sled 1 + mass of sled 2
= 20.0 kg + 14.0 kg
= 34.0 kg
a = F / m
a = 100.04 N / 34.0 kg
≈ 2.95 m/s^2
b) To find the tension in the rope between the sleds, we examine sled 1. The force of friction on sled 1 and the tension in the rope are equal in magnitude but act in opposite directions.
Tension in the rope = force of friction on sled 1
= 58.8 N
Therefore, the magnitude of the tension in the rope between the sleds is 58.8 N.