A 22.0 kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force has a magnitude of 78.0 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 use the given information and apply the laws of physics. Here's how you can find the coefficient of kinetic friction in this scenario:
1. Draw a free-body diagram: Start by drawing a diagram representing the forces acting on the sled. In this case, there are three forces involved - the pulling force, the force of gravity, and the force of kinetic friction.
2. Resolve the pulling force: Decompose the pulling force into its horizontal and vertical components. Use basic trigonometry to determine the magnitude of these components.
- The horizontal component is given by: F_pullx = F_pull * cos(theta), where F_pull is the magnitude of the pulling force and theta is the angle it makes with the horizontal.
- The vertical component is given by: F_pully = F_pull * sin(theta).
3. Calculate the force of friction: As the sled is moving at a constant velocity, the pulling force must balance the force of kinetic friction. Therefore, we can equate the horizontal component of the pulling force to the force of friction: F_pullx = F_friction.
4. Find the normal force: The normal force is the force exerted by the surface on the sled. In this case, since the sled is on a horizontal surface, the normal force (N) is equal to the weight of the sled, which is given by: N = m * g, where m is the mass of the sled and g is the acceleration due to gravity (approximately 9.8 m/s^2).
5. Substitute values and solve for the coefficient of kinetic friction: Now we can substitute the calculated values into the equation F_pullx = F_friction. The equation becomes: F_pull * cos(theta) = u * N, where u is the unknown coefficient of kinetic friction.
- Rearrange the equation to solve for u: u = (F_pull * cos(theta)) / N.
- Substitute the given values: u = (78.0 N * cos(30.0°)) / (22.0 kg * 9.8 m/s^2).
6. Calculate the coefficient of kinetic friction: Plug in the values and solve for u.
- u = (78.0 N * 0.866) / (22.0 kg * 9.8 m/s^2).
- u = 0.298 / 215.6.
- u ≈ 0.00138.
Therefore, the coefficient of kinetic friction in this scenario is approximately 0.00138.
To determine the coefficient of kinetic friction, we can use the following equation:
frictional force = coefficient of kinetic friction × normal force
1. First, let's find the normal force acting on the sled. Since the sled is on a horizontal surface and moving at a constant velocity, the normal force is equal in magnitude and opposite in direction to the gravitational force acting on the sled. The gravitational force can be calculated using the equation:
gravitational force = mass × gravitational acceleration
where the mass is 22.0 kg and the gravitational acceleration is 9.8 m/s².
gravitational force = 22.0 kg × 9.8 m/s² = 215.6 N
Therefore, the normal force acting on the sled is 215.6 N.
2. Next, we can find the frictional force. The frictional force can be calculated using the equation:
frictional force = pulling force × sin(angle)
where the pulling force is 78.0 N and the angle is 30.0°.
frictional force = 78.0 N × sin(30.0°) = 39.0 N
3. Now, substitute the known values into the equation for the frictional force:
39.0 N = coefficient of kinetic friction × 215.6 N
4. Rearrange the equation to solve for the coefficient of kinetic friction:
coefficient of kinetic friction = frictional force / normal force
coefficient of kinetic friction = 39.0 N / 215.6 N = 0.181
Therefore, the coefficient of kinetic friction is approximately 0.181.