# Calculating Forces on Cylinders on Inclines

In summary, the problem involves two identical metal cylinders stacked on top of each other with a weight of 70 lbs and a diameter of 3 ft. The goal is to calculate all forces acting on cylinder A. After drawing a free body diagram and identifying the forces of gravity, normal forces, and reaction forces from cylinder B, the next step would be to sum the forces in the x and y directions. However, it is unclear if the given equations are correct and how to incorporate the diameter.

## Homework Statement

This is a sample exam problem. We have an exam coming up, and I think I better know how to do this problem(the right and quick way).

I'm just copying and pasting the problem.

2. Two identical metal cylinders are stacked as shown in Figure 2. The weight of each cylinder is 70 lb and the diameter of each cylinder is 3 ft. Calculate all forces acting on cylinder A.

View attachment sample exam.bmp

## The Attempt at a Solution

I do not know how to do these type of problems. The circle screws me up for some reason.

I drew a free body diagram, and a force down on each cylinder of (W). Also, cylinder A has two forces normal to the two planes. And, cylinder B also has a force normal to the surface. They both have a force on each other Fab.

I think I'd try to sum the forces in the x and in the y direction.

Fx = Facos(60) + Fbcos(45) + Facos(70)

Fy = Facos(30) + Fbcos(45) + Facos(20) + 70?

I'm not sure if this is even right, nor am I sure what I would do next. I don't understand how to incorporate the diameter either.

The forces acting on cylinder A are two reaction forces from the 'ground' (i.e. normal forces), the force of gravity, and the reaction force from cylinder B. Once you have identified and named these, the rest shouldn't be a problem.

Look at both FBD of A and B seperately

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## 1. What is the purpose of studying cylinders on inclines?

Studying cylinders on inclines helps us understand the principles of force, motion, and energy in a practical and tangible way. It also has real-world applications in fields such as engineering and physics.

## 2. How does the angle of incline affect the behavior of a cylinder?

The angle of incline directly affects the weight distribution and friction of the cylinder. As the angle increases, the weight of the cylinder shifts, causing changes in its motion and potential energy.

## 3. What factors contribute to the rolling motion of a cylinder on an incline?

The rolling motion of a cylinder on an incline is influenced by the force of gravity, the angle of incline, and the mass and shape of the cylinder. Friction also plays a role in slowing down or speeding up the cylinder's motion.

## 4. How do you calculate the potential energy of a cylinder on an incline?

The potential energy of a cylinder on an incline can be calculated using the formula PE = mgh, where m is the mass of the cylinder, g is the acceleration due to gravity, and h is the height of the cylinder on the incline.

## 5. What are some real-life examples of cylinders on inclines?

Some real-life examples of cylinders on inclines include rolling objects such as balls or wheels on ramps, cars driving up or down hills, and objects being transported on conveyor belts or inclined planes.