Final answer:
To find the magnitude of force the worker must apply, we need to consider the forces acting on the crate. The work done on the crate by the normal force is zero, as the crate does not move vertically. The total work done on the crate can be calculated as the sum of the work done by the worker's force, the work done by friction, and the work done by gravity.
Step-by-step explanation:
To find the magnitude of force the worker must apply, we need to consider the forces acting on the crate. The worker must overcome the force of kinetic friction, which is given by the equation F_friction = μ_k * N, where μ_k is the coefficient of kinetic friction and N is the normal force. The normal force can be calculated as N = m * g * cos(θ), where m is the mass of the crate, g is the acceleration due to gravity, and θ is the angle below the horizontal. Thus, the magnitude of force the worker must apply is F = F_friction + m * g * sin(θ).
For the given values, the magnitude of force the worker must apply is approximately 139.25 N.
The work done on the crate by the worker's force can be calculated using the formula W = F * d * cos(θ), where d is the distance the crate is pushed.
The work done on the crate by friction can be calculated as W_friction = F_friction * d * cos(180°), since the force of friction acts opposite to the displacement.
The work done on the crate by the normal force is zero, as the crate does not move vertically.
The work done on the crate by gravity can be calculated as W_gravity = m * g * d * sin(θ), as gravity acts vertically downwards.
The total work done on the crate can be calculated as the sum of the work done by the worker's force, the work done by friction, and the work done by gravity.