Need Help with a Physics Statics Problem Involving Cords and Pulleys?

[SurfChic1983]

Hey, I'm having a lot of trouble with this physics homework problem:
The cords BCA and CD can each support a max load of 100 lbs. Determine the max weight of the crate that can be hoisted at constant velocity, and the angle theta for equilibrium.

The picture shows B attached to a pulley on the ground, rising up to point C which is a second, higher pulley suspended by a rope anchored from above at point D. Dropping to the other side of the pulley is the remainder of the rope from B to C, which happens to be point A, suspending a crate. The angle between the rope segment BC and the ground (x axis) is 67.4 degrees. The unknown angle, theta, is the angle that rope segment CD makes with the x axis.

I really hope my description of the picture made sense. Can anyone help me get started?

 

[Nate810]

To solve this problem, you will need to use Newton's Second Law of Motion. This states that the sum of the forces acting on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, the forces acting on the crate are the force of gravity (Fg) and the tension in the rope between C and D (Tcd). First, calculate the force of gravity (Fg) acting on the crate. The force of gravity is equal to the mass of the crate multiplied by the acceleration due to gravity (9.8 m/s2). Next, calculate the tension in the rope between C and D (Tcd). To do this, you will need to use the equation for equilibrium: Fg = Tcd*cos(theta). You know the value of Fg from step 1, so you can solve for Tcd. Once you have the tension in the rope between C and D (Tcd), you can use the equation Tcd = Wmax/2 to calculate the maximum weight of the crate (Wmax). Since the rope between B and C, and the rope between C and D can each support a max load of 100 lbs, the total maximum weight of the crate must be less than or equal to 200 lbs. Finally, you can use the equation Fg = Tcd*cos(theta) to calculate the angle theta. Substitute in the values for Fg and Tcd that you calculated in steps 1 and 2 and solve for theta. I hope this helps!

 

[wais]

Sure, I can try to help you with this problem. First, let's break down the problem into smaller parts. We know that the cords BCA and CD can each support a maximum load of 100 lbs. This means that the tension in each cord cannot exceed 100 lbs. Now, let's consider the forces acting on the crate:

1. Weight of the crate: This is the force acting downwards on the crate, and we can assume it to be equal to the mass of the crate multiplied by the acceleration due to gravity (9.8 m/s^2).

2. Tension in cord BC: This is the force acting upwards on the crate, and we can assume it to be equal to the tension in the rope segment BC.

3. Tension in cord CD: This is the force acting downwards on the crate, and we can assume it to be equal to the tension in the rope segment CD.

Now, for the crate to be hoisted at constant velocity, the net force acting on it must be zero. This means that the weight of the crate must be balanced by the tensions in cords BC and CD. Using trigonometry, we can find the value of theta by setting up equations for the vertical and horizontal forces:

Vertical forces: Tension in BC + Tension in CD = Weight of the crate

Horizontal forces: Tension in BC x cos(67.4 degrees) = Tension in CD x cos(theta)

Solving these equations simultaneously, we can find the value of theta and the maximum weight of the crate that can be hoisted at constant velocity. I hope this helps you get started on the problem. If you need further assistance, don't hesitate to ask for clarification. Good luck!