Solving Statics Rope Problem: Finding Force & Angle

[Jstew]

Homework Statement

Using a uniform strut, a rigid brace hinged at the floor, a
person holds a 30-kg engine in equilibrium while it is being
repaired. The strut has a mass of 12.5 kg. A smooth rope passes
over a pulley at the end of the strut. (a) What is
the force exerted on the rope by the person? (Specify the direction
of this force by calculating the angle theta that the rope
makes with the horizontal.) (b)What forces are exerted by the
strut?

Homework Equations

Fx=0
Fy=0
T=rF=0

The Attempt at a Solution

Looking at the engine, Fy=0 so Tension=mg. I don't know where to go from here.

 

[tiny-tim]

Hi Jstew!

Looking at the engine, Fy=0 so Tension=mg.

Well, that's the answer to (a), isn't it?

For (b), start by taking moments about the hinge.

 

[thomate1]

As a scientist, the approach to solving this statics rope problem would be to first draw a free body diagram of the system, clearly labeling all the forces acting on the objects. From the given information, we know that the person is holding the engine in equilibrium, so the net force in both the x and y direction must be zero. This means that the force exerted by the person on the rope must be equal and opposite to the weight of the engine.

To find the magnitude of the force, we can use the equation F=ma, where F is the net force, m is the mass, and a is the acceleration. In this case, the net force is the force exerted by the person on the rope, and the mass is the weight of the engine. Plugging in the values, we get F=30kg*9.8m/s^2=294N.

To find the angle theta, we can use the equation tan(theta)=Fy/Fx. Since Fy=mg and Fx=T, we get tan(theta)=mg/T. Plugging in the values, we get tan(theta)=30kg*9.8m/s^2/294N, which simplifies to tan(theta)=1. Therefore, theta=45 degrees.

For part (b), the forces exerted by the strut can be found by using the equation F=ma. In this case, the mass is the mass of the strut, and the acceleration is zero since the strut is not moving. Therefore, the forces exerted by the strut are equal and opposite to the forces exerted by the person on the rope. The magnitude of these forces is 294N, and the direction is perpendicular to the strut and parallel to the floor.