A 29.8-kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force has a magnitude of 88.8 N and is directed at an angle of 39 ° above the horizontal. Determine the coefficient of kinetic friction.
upword force=88.8*cos39
forward force= 88.8 sin39
frictionforce=forward force
mu*normal=88.8 sin39
mu(29.8*g-upwardforce)=88.8 sin39
calculate mu.
To determine the coefficient of kinetic friction, we need to consider the forces acting on the sled and use the concept of equilibrium. Since the sled is moving at a constant velocity, the net force acting on it is zero.
First, we need to resolve the pulling force into horizontal and vertical components. The horizontal component of the pulling force can be found using trigonometry:
Horizontal component = Magnitude of the pulling force * cos(angle)
Horizontal component = 88.8 N * cos(39 °)
Horizontal component = 88.8 N * 0.766 (rounded to 3 decimal places)
Horizontal component = 68.000 N (rounded to 3 decimal places)
Next, let's calculate the gravitational force acting on the sled. The gravitational force can be found using the mass of the sled and the acceleration due to gravity:
Gravitational force = Mass * Acceleration due to gravity
Gravitational force = 29.8 kg * 9.8 m/s²
Gravitational force = 292.4 N
Since the sled is moving with a constant velocity, the net force acting on it is zero. Therefore, the horizontal component of the pulling force must balance the force of kinetic friction.
Horizontal component of the pulling force = Force of kinetic friction
68.000 N = Force of kinetic friction
Now, we can determine the coefficient of kinetic friction using the formula:
Force of kinetic friction = Coefficient of kinetic friction * Normal force
Since the sled is on a horizontal surface, the normal force is equal to the gravitational force:
Force of kinetic friction = Coefficient of kinetic friction * Gravitational force
68.000 N = Coefficient of kinetic friction * 292.4 N
Coefficient of kinetic friction = 68.000 N / 292.4 N
Coefficient of kinetic friction = 0.232 (rounded to 3 decimal places)
Therefore, the coefficient of kinetic friction between the sled and the horizontal surface is approximately 0.232.