A 15.5-kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force has a magnitude of 76.7 N and is directed at an angle of 27 ° above the horizontal. Determine the coefficient of kinetic friction.
M*g = 15.5 * 9.8 = 151.9 N.=Wt. 0f sled.
Fn = 151.9 - 76.7*sin27 = 117 N.
Fap-Fk = M*a.
76.7*Cos27-Fk = M*0 = 0.
Fk = 68.3 N.=Force of kinetic friction.
u = Fk/Fn 68.3/117 = 0.584.
To determine the coefficient of kinetic friction, we need to consider the forces acting on the sled.
1. The pulling force: The pulling force has a magnitude of 76.7 N and is directed at an angle of 27° above the horizontal. We need to resolve this force into its horizontal and vertical components.
The vertical component of the pulling force: F_vertical = F * sin(theta) = 76.7 N * sin(27°)
The horizontal component of the pulling force: F_horizontal = F * cos(theta) = 76.7 N * cos(27°)
2. The force of kinetic friction: Since the sled is moving at a constant velocity, the force of kinetic friction must be equal in magnitude and opposite in direction to the horizontal component of the pulling force.
F_friction = F_horizontal
3. The normal force: The normal force is the force exerted by the surface on the sled to support its weight. Since the sled is on a horizontal surface and is not accelerating vertically, the normal force is equal in magnitude and opposite in direction to the vertical component of the pulling force.
N = F_vertical
4. The weight of the sled: The weight of the sled is equal to its mass multiplied by the acceleration due to gravity.
Weight = mass * g = 15.5 kg * 9.8 m/s^2
Now, to determine the coefficient of kinetic friction, we can use the formula:
coefficient of kinetic friction = F_friction / N
Substituting the values we have:
coefficient of kinetic friction = (F_horizontal) / (F_vertical)
coefficient of kinetic friction = (76.7 N * cos(27°)) / (76.7 N * sin(27°))
By evaluating this expression, we can determine the coefficient of kinetic friction.