# Force and Motion Sliding/Hanging Blocks

• Shatzkinator
In summary, the chain of masses is pulled down by the force of gravity, and the tension in the cord is the resultant force acting on mass A.
Shatzkinator

## Homework Statement

In Figure 5-52, three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The masses are mA = 30.0 kg, mB = 42.0 kg, and mC = 14.0 kg. When the assembly is released from rest, (a) what is the tension in the cord connecting B and C, and (b) how far does A move in the first 0.260 s (assuming it does not reach the pulley)?

... there is block a which is on the surface and block b and c are hanging over the edge pulling it down.

fnet = ma
T = ma
Fgc - T = ma
Fgb - T = ma

## The Attempt at a Solution

I'm not sure what I'm supposed to do, i thought of subtracting the equations, but i don't think that will work based on what I'm looking at and i don't think substitution of a variable t or a will work... help?

To answer both questions, you need to determine the acceleration of the system. This requires finding the net force of the system. This can be done with a bit of a shortcut: treat all forces in one, not two dimensions. The downward force on the hanging mass is the "same direction" as the sideways forces toward the pulley. It's not exactly correct, but it works out if the pulley is massless and frictionless.

Note: when summing all forces, the tensions are interior, and therefore do not contribute to the net force on the system.

There is no mention of friction force - I guess you assume it is zero.
The force causing the whole chain of masses to accelerate is the force of gravity on the hanging masses. Use that to calculate the acceleration.

The tension in the cord is the force acting on mass A, causing it to accelerate at the rate you have already calculated.

I don't seem to be getting the correct answer... this is what i did for the system:

The only forces i see that contribute to the acceleration are Fgb and Fgc... they are 411.6 and 137.2 respectively. Fgb + Fgc = ma... solving this i get 9.8 m/s^2 obviously gravity. But when i do T = ma on block a to solve for tension using 9.8, i don't ge tthe correct answer??

edit: wait i didn't include the mass of block a for calculating the acceleration. Thats probably my mistake.

edit 2: Yes it was my mistake! =)
Thanks for the help!

Last edited:

## What is force and motion?

Force and motion refer to the physical concepts of how objects interact with each other and how they move in response to those interactions. Force is a push or pull on an object, while motion is the change in position or orientation of an object over time.

## What is the difference between sliding and hanging blocks?

Sliding blocks refer to objects that are being pushed or pulled along a surface, while hanging blocks refer to objects that are suspended or hanging from a support. The main difference between the two is the direction of the force and the resulting motion.

## What factors affect the force and motion of sliding/hanging blocks?

The force and motion of sliding/hanging blocks can be affected by various factors, such as the mass of the blocks, the surface they are sliding on, the amount of force applied, and the friction between the blocks and the surface. Other factors may include the angle of the surface, air resistance, and the shape or size of the blocks.

## How do you calculate the force and motion of sliding/hanging blocks?

The force and motion of sliding/hanging blocks can be calculated using Newton's laws of motion. The first law states that an object at rest will remain at rest, and an object in motion will continue moving in a straight line at a constant speed unless acted upon by a net force. The second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

## What are some real-world applications of force and motion in sliding/hanging blocks?

The concepts of force and motion in sliding/hanging blocks have many real-world applications, such as in engineering and construction. Understanding the forces and motions involved in sliding/hanging blocks can help design structures that can withstand external forces, such as wind or earthquakes. The principles of force and motion are also crucial in the development of technologies, such as elevators, escalators, and roller coasters.

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