A 2000 N sled is pulled along a horizontal surface with a constant force by means of a rope that makes an angle of 30.0o with the horizontal. If the tension in the rope is 500 N and there is 100 N of frictional force between the sled and the surface, find the work done on the sled when it is pulled through the distance of 40.0m
25N
To find the work done on the sled, we need to determine the net force acting on the sled and multiply it by the distance it is pulled.
The net force is the vector sum of the tension force and the frictional force:
Net force = Tension force - Frictional force
Given:
Tension force (T) = 500 N
Frictional force (f) = 100 N
Substituting the values, we get:
Net force = 500 N - 100 N
Net force = 400 N
Next, we need to find the horizontal component of the net force. This can be calculated using trigonometry, as the force is acting at an angle of 30.0o with the horizontal:
Horizontal component of the net force = Net force * cos(θ)
θ is the angle of 30.0o
Horizontal component of the net force = 400 N * cos(30.0o)
Horizontal component of the net force = 400 N * 0.866
Horizontal component of the net force = 346.4 N
Now that we have the net force in the horizontal direction, we can calculate the work done:
Work done = Net force * distance
Given:
Distance (d) = 40.0 m
Work done = 346.4 N * 40.0 m
Work done = 13856 J
Therefore, the work done on the sled when it is pulled through a distance of 40.0 m is 13856 J.