Two girls pull a 15 kg sled, each with her own rope. They pull horizontally at an angle of 30 degrees from each other with identical forces of 25 N each. The coefficient of friction between the snow and the sled is 0.1.
The acceleration of gravity is 9.8 m/s2 . What is the acceleration of the sled? Answer in units of m/s2.
To find the acceleration of the sled, we'll start by analyzing the forces acting on it and then apply Newton's second law of motion.
Let's break down the forces acting on the sled:
1. Tension forces: Each girl exerts a force of 25 N on the sled. Since the forces are applied at an angle of 30 degrees from each other, their horizontal components will add up to create the net force in the horizontal direction.
F_net_horizontal = 2 * (25 N * cos(30)) = 2 * (25 N * (√3/2)) = 2 * (25 N * (√3/2)) = 75√3 N
2. Friction force: The coefficient of friction between the snow and the sled is given as 0.1. Since the sled is being pulled horizontally, the friction force acts in the opposite direction to the net applied force.
F_friction = coefficient of friction * normal force
Normal force = mass * gravity = 15 kg * 9.8 m/s^2 = 147 N
F_friction = 0.1 * 147 N = 14.7 N
Now, we can apply Newton's second law of motion:
F_net_horizontal - F_friction = mass * acceleration
(75√3 N) - (14.7 N) = 15 kg * acceleration
Simplifying the equation:
75√3 N - 14.7 N = 15 kg * acceleration
60√3 N = 15 kg * acceleration
Dividing both sides by 15 kg:
4√3 m/s^2 = acceleration
Therefore, the acceleration of the sled is approximately 4√3 m/s^2.