A 23.0 kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force has a magnitude of 79.0 N and is directed at an angle of 30.0° above the horizontal. Determine the coefficient of kinetic friction.
To determine the coefficient of kinetic friction, we need to understand the forces acting on the sled.
The pulling force applied to the sled has a magnitude of 79.0 N and is directed at an angle of 30.0° above the horizontal. This force can be broken down into two components: the vertical component and the horizontal component.
The vertical component of the pulling force is given by the equation F_vertical = F * sin(theta), where F is the magnitude of the pulling force and theta is the angle above the horizontal. Plugging in the values, we get F_vertical = 79.0 N * sin(30.0°) = 39.5 N.
Since the sled is moving at a constant velocity, there must be an opposing force that balances out the pulling force. This opposing force is the force of kinetic friction between the sled and the horizontal surface.
The force of kinetic friction can be calculated using the equation f_kinetic = coefficient * N, where coefficient is the coefficient of kinetic friction and N is the normal force acting on the sled.
In this case, the normal force N is equal to the weight of the sled, which can be calculated using the equation N = m * g, where m is the mass of the sled and g is the acceleration due to gravity (9.8 m/s^2).
Plugging in the values, we get N = 23.0 kg * 9.8 m/s^2 = 225.4 N.
Since the sled is being pulled horizontally, the normal force is equal to the vertical component of the pulling force. Therefore, the normal force N is 39.5 N.
Now we can calculate the force of kinetic friction. Using the equation f_kinetic = coefficient * N and plugging in the values, we get f_kinetic = coefficient * 39.5 N.
Since the sled is moving at a constant velocity, the force of kinetic friction is equal in magnitude and opposite in direction to the pulling force. Therefore, f_kinetic = 79.0 N.
Plugging in this value, we get 79.0 N = coefficient * 39.5 N.
Solving for the coefficient of kinetic friction, we get coefficient = 79.0 N / 39.5 N = 2.00.
Therefore, the coefficient of kinetic friction between the sled and the horizontal surface is 2.00.
YOu have two things here: zero acceleration, and the pulling force upward is helping reduce friction (making normal force less).
vertical component of pulling: 79Sin30, which reduces weight of sled down.
Normal force downward: mg-73sin30
friction force=mu*normal=mu*(mg-73sin30)
horizontal force= 73cos30
netforce=ma
pulling forcehorizontal-frictionforce=0
73cos30-mu(mg-73sin30)=0
solve for mu.