Understanding Pulleys in a Frictionless System

In summary: F=maF=(7.4)(3.0)F=22.2 NIn summary, on a frictionless surface, a 47N weight is pulled by a frictionless pulley attached to a 25N weight by a cord. The acceleration of the 47N weight is approximately 3.0 m/s² and the force on the cord is 22.2 N. These calculations are based on Newton's second law, F=ma.
  • #1
kashiark
210
0

Homework Statement


A 47N weight is pulled on a frictionless surface by a frictionless pulley that is attached to a 25N weight by a cord.
A. What is the acceleration of the 47N weight?
B. What is the force on the cord?

Homework Equations


F=ma


The Attempt at a Solution


A.
25=(47/9.8)a
a= about 5.2 m/s²
B. no clue whatsoever
 
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  • #2
Hi kashiark! :smile:

(is this a horizontal surface? is the weight hanging vertically off the end? :confused:)

Your A is wrong.

Start again …

write out Newton's second law three times: once for the 47N weight on its own, once for the 25N weight on its own, and once for the pair of weights together. :smile:
 
  • #3
I'm understanding the problem to mean that one weight is on the ground and the other end is in the air, but if the heavier end is on the ground, wouldn't the cord just go limp and pull the lighter weight up to the top of the pulley?

47=9.8m
m= 4.8

25=9.8m
m= 2.6

I'm not sure how I would compose the third equation.
 
  • #4
kashiark said:
I'm understanding the problem to mean that one weight is on the ground and the other end is in the air, but if the heavier end is on the ground, wouldn't the cord just go limp and pull the lighter weight up to the top of the pulley?

No, that must be wrong …
kashiark said:
A 47N weight is pulled on a frictionless surface …

the question clearly states that the weight stays on the surface …

I assume the rope starts horizontal, then goes over the pulley and hangs down vertically.
 
  • #5
Your understanding definitely makes more sense though, but if that's the case, then the weight on the vertical cord would be pulling the weight on the surface horizontally, and you wouldn't have to account for its weight at all in A because it's pulling vertically right?
 
  • #6
Ok, I just read that, and it's very ambiguous. Let's call WA the weight that's on the surface and WB the weight that's not. In part A, you wouldn't need to include WA's weight because it would be pulling it down, and WB's weight would be pulling it horizontally right?
 
  • #7
Physics is equations.

Stop waffling … write out the equations for Newton's second law three times … what do you get?
 
  • #8
47=9.8m
m= 4.8

25=9.8m
m= 2.6

Ok I'll stop for now, but I would greatly appreciate it if you could explain it to me. How's this:
22=a(2.6+4.8)
22=7.4a
a=3.0 m/s²
 

FAQ: Understanding Pulleys in a Frictionless System

1. What is a pulley problem?

A pulley problem is a type of physics problem that involves using the principles of mechanics to solve for unknown quantities in a system of pulleys and ropes. These problems typically require knowledge of concepts such as force, tension, and mechanical advantage.

2. How do I approach solving a pulley problem?

The first step in solving a pulley problem is to draw a free-body diagram of the system, identifying all the forces acting on each object. Then, use the equations of motion and the principles of mechanics to set up and solve a system of equations. It can also be helpful to break the problem down into smaller, simpler parts.

3. What is the difference between a single pulley and a compound pulley?

A single pulley is a simple machine that changes the direction of a force, while a compound pulley is made up of multiple pulleys that work together to amplify or reduce the force needed to lift an object. Compound pulleys are more complex and can provide a greater mechanical advantage.

4. How do I calculate the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system is equal to the ratio of the output force to the input force. In other words, it is the amount that the pulley system multiplies the force applied. To calculate it, divide the weight of the load by the effort force applied.

5. Can I use the same approach to solve all pulley problems?

While there are certain steps and principles that can be applied to most pulley problems, each problem may have its own unique variables and factors to consider. It is important to carefully read and understand the given information and approach each problem with a critical thinking mindset.

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