Step-by-step explanation:
To calculate the net work done on the block, we need to first calculate the work done by the applied force, and then subtract the work done by friction.
1. Work done by the applied force:
The component of the applied force that is in the direction of motion is given by:
F_parallel = F_applied * sin θ
where θ is the angle of inclination. Plugging in the given values, we get:
F_parallel = 80N * sin 30°
F_parallel = 40N
The work done by the applied force is given by:
W_applied = F_parallel * d
where d is the length of the inclined plane. Plugging in the given values, we get:
W_applied = 40N * 20m
W_applied = 800J
2. Work done by friction:
The force of kinetic friction is given by:
F_friction = μ_k * N
where μ_k is the coefficient of kinetic friction, and N is the normal force. The normal force is equal to the weight of the block:
N = m * g
where m is the mass of the block, and g is the acceleration due to gravity (taken as 9.8 m/s²). Plugging in the given values, we get:
N = 5kg * 9.8 m/s²
N = 49N
Therefore, the force of kinetic friction is given by:
F_friction = 0.25 * 49N
F_friction = 12.25N
The work done by friction is given by:
W_friction = F_friction * d
Plugging in the given value of d, we get:
W_friction = 12.25N * 20m
W_friction = 245J
3. Net work done:
The net work done on the block is given by:
Net work = W_applied - W_friction
Plugging in the values we calculated earlier, we get:
Net work = 800J - 245J
Net work = 555J
Therefore, the net work done on the block is 555 joules.