Answer:
Step-by-step explanation:
(a) The work done by gravity can be calculated as the product of the force of gravity and the distance over which it acts. The force of gravity can be found by multiplying the mass of the block by the acceleration due to gravity, g = 9.81 m/s^2.
F gravity = m * g = 35 kg * 9.81 m/s^2 = 343.35 N
The component of the force of gravity acting parallel to the inclined plane is:
F parallel = F gravity * sin(37°) = 343.35 N * sin(37°) = 205.72 N
The work done by gravity is:
W gravity = F parallel * d = 205.72 N * 8 m = 1645.76 J
(b) The normal force is the force exerted by the inclined plane perpendicular to the surface of the block. Since the block is sliding down the inclined plane, the normal force is less than the weight of the block.
The normal force can be found by resolving the force of gravity into its components perpendicular and parallel to the inclined plane. The component perpendicular to the inclined plane is:
F perpendicular = F gravity * cos(37°) = 343.35 N * cos(37°) = 271.60 N
The force of kinetic friction is given by:
F friction = μ_k * F normal
where μ_k is the coefficient of kinetic friction and F normal is the normal force. The work done by the force of friction can be found as:
W friction = F friction * d = μ_k * F normal * d
Substituting the values given:
W friction = 0.3 * 271.60 N * 8 m = 651.84 J
The work done by the normal force can be found as the difference between the work done by gravity and the work done by friction:
W normal = W gravity - W friction = 1645.76 J - 651.84 J = 993.92 J
Therefore, the work done by the normal force is 993.92 J.