A sledge loaded with bricks has a total mass of 18.9 kg and is pulled at constant speed by a rope inclined at 19.3° above the horizontal. The sledge moves a distance of 19.8 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. What is the tension on the rope?
To find the tension on the rope, we need to analyze the forces acting on the sledge.
First, let's resolve the weight component of the sledge. The weight of the sledge can be calculated using the formula:
Weight (W) = mass (m) * acceleration due to gravity (g)
Given that the mass of the sledge is 18.9 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight:
Weight (W) = 18.9 kg * 9.8 m/s²
Next, let's calculate the normal force acting on the sledge. The normal force is a reaction force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal in magnitude to the weight since the sledge is at rest.
Normal force (N) = Weight (W)
Now, let's determine the frictional force acting on the sledge. The frictional force can be calculated using the formula:
Frictional force (f) = coefficient of friction (μ) * Normal force (N)
Given that the coefficient of kinetic friction is 0.500, we can calculate the frictional force:
Frictional force (f) = 0.500 * Normal force (N)
Next, let's determine the horizontal force acting on the sledge. The horizontal force is the force exerted by the tension in the rope and is equal to the sum of the frictional force and the component of the weight parallel to the horizontal surface.
Horizontal force = Frictional force + Component of weight parallel to the surface
The component of the weight parallel to the surface can be calculated using trigonometry:
Component of weight parallel to the surface = Weight (W) * sin(θ)
where θ is the angle of inclination with respect to the horizontal surface. In this case, the angle of inclination is given as 19.3°.
Now that we have the horizontal force, we can equate it to the tension on the rope:
Tension on the rope = Horizontal force
By substituting the calculated values into the equation, you can find the tension on the rope.