A 19.5 kg block is dragged over a rough, horizontal surface by a constant force of 110 N acting at an angle of angle 31.1◦ above the horizontal. The block is displaced 6.74 m,and the coefficient of kinetic friction is 0.156.
What is the net work done on the block?
Answer in units of J.
The work done is the component of the dragging force along the direction of motion, 110 cos 31.1, multiplied by 5.64 m. You do not need to know the friction coefficient. Work that does not get converted to frictional heat will become kinetic energy
To find the net work done on the block, we need to calculate the work done by the applied force and the work done by the friction force, and then subtract the latter from the former.
1. Work done by the applied force:
The work done by a force can be calculated using the formula:
Work = Force × displacement × cos(θ),
where Force is the magnitude of the force, displacement is the magnitude of the displacement, and θ is the angle between the force and the displacement.
In this case, the magnitude of the applied force is 110 N, the displacement is 6.74 m, and the angle is 31.1 degrees. Let's calculate the work done by the applied force:
Work_applied = 110 N × 6.74 m × cos(31.1°)
Work_applied = 724.39 J
2. Work done by the friction force:
The work done by friction can be calculated using the formula:
Work = Force_friction × displacement × cos(180°),
where Force_friction is the magnitude of the friction force, displacement is the magnitude of the displacement, and cos(180°) equals -1 (since the angle between the force and displacement is 180 degrees).
The friction force can be calculated using the formula:
Force_friction = coefficient of friction × normal force,
where the normal force is the force perpendicular to the surface, which is equal to the weight of the block.
The normal force can be calculated using the formula:
Normal force = mass × gravity,
where mass is the mass of the block and gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the mass of the block is 19.5 kg and the coefficient of kinetic friction is 0.156. Let's calculate the work done by the friction force:
Normal force = 19.5 kg × 9.8 m/s^2
Normal force = 191.1 N
Force_friction = 0.156 × 191.1 N
Force_friction = 29.82 N
Work_friction = 29.82 N × 6.74 m × cos(180°)
Work_friction = -200.68 J (Note: The negative sign indicates that the friction force is opposing the displacement.)
3. Net work done:
Net work done = Work_applied - Work_friction
Net work done = 724.39 J - (-200.68 J)
Net work done = 925.07 J
Therefore, the net work done on the block is 925.07 J.