A worker stands still on a roof sloped at an angle of 43° above the horizontal. He is prevented from slipping by a static frictional force of 520 N. Find the mass of the worker.

I guess he is JUST prevented from slipping

normal force = m g cos 43
force down slope = m g sin 43
so
m g sin 43 = 520

To find the mass of the worker, we need to use the equation relating static friction to the normal force:

F_friction = μ * F_normal

where F_friction is the static frictional force, μ is the coefficient of friction, and F_normal is the normal force.

In this case, the static frictional force is 520 N, and the angle of the roof with respect to the horizontal is 43°. We can find the normal force by using the equation:

F_normal = mg * cos(θ)

where m is the mass of the worker, g is the acceleration due to gravity (approximately 9.8 m/s²), and θ is the angle of the roof.

Substituting the given values into the equations, we have:

F_friction = μ * F_normal
520 N = μ * mg * cos(43°)

Solving for the mass, we get:

m = (520 N) / (μ * g * cos(43°))

Note that we still need the coefficient of friction (μ) to find the mass. If you have the value of the coefficient of friction, please provide it.

To find the mass of the worker, we can use the concept of static equilibrium. In a state of static equilibrium, the sum of all the forces acting on an object is zero.

Here's how we can approach this problem:

1. Draw a free-body diagram to represent all the forces acting on the worker. On the diagram, indicate the weight of the worker (mg), the normal force (N), and the static frictional force (fs).

The weight of the worker (mg) acts vertically downwards.
The normal force (N) acts perpendicular to the slope of the roof.
The static frictional force (fs) acts parallel to the slope of the roof and opposes the tendency of the worker to slip.

2. Resolve the forces along the vertical and horizontal directions.

Along the vertical direction, the weight of the worker (mg) can be resolved into two components:
- The component perpendicular to the slope, which is equal to N.
- The component parallel to the slope, which is equal to mgsin(43°).

Along the horizontal direction, the static frictional force (fs) is acting in the opposite direction to the component of the weight parallel to the slope.

3. Set up equations based on the condition of static equilibrium.

In the vertical direction:
N - mgsin(43°) = 0

In the horizontal direction:
fs = 520 N

4. Solve the equations to find the mass of the worker.

From the equation N - mgsin(43°) = 0, we can solve for N:
N = mgsin(43°)

Substitute this expression for N into the equation fs = 520 N:
fs = 520 (mgsin(43°))

Equate the two expressions for fs:
mgsin(43°) = 520 N

Solve for the mass of the worker (m):
m = (520 N) / (gsin(43°))

Plug in the value of the acceleration due to gravity (g ≈ 9.8 m/s^2) and solve for m.

By following these steps, you should be able to find the mass of the worker by plugging in the appropriate values and performing the calculations.