A block of weight 20 N is pushed with a force of 30 N through a horizontal distance of 5 m using a stick which is at an angle of 37° from the horizontal as shown. The coefficient of kinetic friction µk between the table and the block is 0.25. For your own reference, draw a force diagram of the block.
A) What is the normal force on the block?
B) What is the frictional force between the block and the table?
C) What is the work done by the frictional force?
D) What is the net work done on the block?
Sorry, I can't draw a force diagram of the box.
The sum of the forces in the y-direction is zero:
N - 20 + 30*sin(37) = 0
Solve for N, the normal force
B) The frictional force between the block and the table is defined as µk*N = 0.25*N
C) The work done by the frictional force is 0.25*N*5
D) The work done by the pushing force is 30*cos(37); The net work is 30*5*cos(37) - 0.25*N*5
To solve this problem, we will first draw a force diagram for the block.
Force diagram:
1. Start by drawing a horizontal line to represent the surface of the table.
2. Draw an upward arrow from the horizontal line to represent the normal force (N). This force counteracts the weight of the block and has the same magnitude but opposite direction.
3. Draw a downward arrow to represent the weight (W) of the block. The weight of the block can be calculated by multiplying the mass of the block by the acceleration due to gravity (9.8 m/s^2).
4. Draw a diagonal arrow to represent the applied force (F) of 30 N. This force is at an angle of 37° from the horizontal.
5. Finally, draw an arrow opposing the direction of motion to represent the frictional force (f). This force is directed opposite to the applied force and is determined using the coefficient of kinetic friction (µk) and the normal force (N).
A) To find the normal force (N), we know that it is equal in magnitude but opposite in direction to the weight of the block. The weight can be calculated using the formula W = mg, where m is the mass of the block and g is the acceleration due to gravity. Once we know the weight, we can determine the normal force.
B) The frictional force (f) can be calculated using the formula f = µk * N, where µk is the coefficient of kinetic friction and N is the normal force.
C) The work done by the frictional force can be calculated using the formula W = f * d, where f is the frictional force and d is the distance over which the block is moved.
D) The net work done on the block is equal to the work done by the applied force (F) minus the work done by the frictional force (W). This can be calculated using the formula net work = F * d - W.
To find the answers to these questions, we need to know the mass of the block.