A 18 kg sled is pulled a child holding a rope with an applied force at an angle of 45 degrees with the ground. The normal force is 50N and the sled is accelerating at 6 m/s2. What is the force applied to the sled? What is the coefficient of friction?
To find the force applied to the sled, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the sled has a mass of 18 kg and is accelerating at 6 m/s^2. Therefore, the force applied to the sled can be calculated as follows:
Force applied to the sled = mass * acceleration
= 18 kg * 6 m/s^2
= 108 N
So, the force applied to the sled is 108 Newtons.
To find the coefficient of friction, we need to consider the relationship between the normal force and the frictional force. The frictional force can be calculated using the equation F_friction = coefficient of friction * normal force.
In this case, the normal force is given as 50 N. We know that the sled is accelerating, which means there must be a net force in the direction opposite to the applied force. This net force is the sum of the frictional force and the component of the applied force in the horizontal direction.
Since the sled is accelerating, the net force is given by the following equation:
Net force = Force applied to the sled - Frictional force
Applying Newton's second law again, we have:
Net force = mass * acceleration
So we can rewrite the equation as:
Force applied to the sled - Frictional force = mass * acceleration
Rearranging the equation, we get:
Frictional force = Force applied to the sled - mass * acceleration
Plugging in the known values, we get:
Frictional force = 108 N - (18 kg * 6 m/s^2)
= 108 N - 108 N
= 0 N (since the sled is accelerating)
Since the frictional force is zero, this means that there is no friction acting on the sled. Therefore, the coefficient of friction is zero.