Starting from rest, a 5.00 kg block slides 2.50 m down a rough 30.0 degree incline. The coefficient of kinetic friction between block and the incline is .436. Determine the work done by the friction force between block and incline and the work done on the normal force
See your 10-12-11,5:27pm post for solution.
To determine the work done by the friction force and the work done on the normal force, we need to first find the net force acting on the block as it moves down the incline.
1. Start by finding the gravitational force acting on the block. The gravitational force can be calculated using the formula:
Gravitational force = mass × acceleration due to gravity
Gravitational force = 5.00 kg × 9.8 m/s²
Gravitational force = 49.0 N
2. Next, find the component of the gravitational force acting parallel to the incline. This can be found using the formula:
Parallel force = Gravitational force × sin(θ)
Parallel force = 49.0 N × sin(30.0°)
Parallel force = 24.5 N
3. Calculate the normal force acting perpendicular to the incline. The normal force can be found using the formula:
Normal force = Gravitational force × cos(θ)
Normal force = 49.0 N × cos(30.0°)
Normal force = 42.4 N
4. Calculate the frictional force. The frictional force can be found using the formula:
Frictional force = coefficient of kinetic friction × Normal force
Frictional force = 0.436 × 42.4 N
Frictional force = 18.5 N
5. Calculate the net force. Since the block is moving down the incline, the net force is the difference between the parallel force and the frictional force:
Net force = Parallel force - Frictional force
Net force = 24.5 N - 18.5 N
Net force = 6.0 N
6. Finally, calculate the work done by the friction force and the work done on the normal force:
Work done by friction force = Frictional force × distance
Work done by friction force = 18.5 N × 2.50 m
Work done by friction force = 46.25 J
Work done on normal force = Normal force × distance
Work done on normal force = 42.4 N × 2.50 m
Work done on normal force = 106 J
Therefore, the work done by the friction force is 46.25 J, and the work done on the normal force is 106 J.