Acceleration of masses in a pulley system

In summary, the conversation involved discussing an equation for determining acceleration in a system with two blocks connected by a string. The speaker initially thought their answer was incorrect, but then realized that due to the string being inextensible, the acceleration for both blocks would be the same. They also mentioned a mistake in their equation involving the denominator and the sign of the friction term.
  • #1
jisbon
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Homework Statement
2 masses on each side of the inclined plane. Coefficient of kinetic friction = 0.3, held by an inextensible string.
Masses of blocks as labelled on the diagram
Relevant Equations
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1573733245458.png


So I figured out the equation, but it is probably wrong because the answer doesn't tally.
Since the string is inextensible, I can assume that tension is the same for both sides, and acceleration for both masses is the same too So:
I can say that the acceleration of 2kg block =acceleration of 7kg block

$$\dfrac {7g\sin 40-T}{2+7}=\dfrac {T+\left( 0.3\right) \left( 2g\cos 50\right) -2g\sin 50}{7+2} $$

I got T = 29.36N, and used one of the equation to get my acceleration. However, it seems to be wrong :/

Is there something wrong with my equation? Thanks
 
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  • #2
The denominator of the first terms should be 7 and the denominator of the 2nd term should be 2, and the sign of the friction term should be negative.
 
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  • #3
Chestermiller said:
The denominator of the first terms should be 7 and the denominator of the 2nd term should be 2, and the sign of the friction term should be negative.
Mistaken it for static friction and the massess too. Thanks for the help
 

1. What is a pulley system and how does it work?

A pulley system is a simple machine that uses a rope or belt to change the direction of a force. It works by transferring the applied force from one end of the rope to the other, allowing heavy objects to be lifted with less effort.

2. What is acceleration and how is it related to mass in a pulley system?

Acceleration is the rate at which an object's velocity changes over time. In a pulley system, the acceleration of a mass is directly related to the force applied and the mass of the object. The larger the mass, the slower the acceleration will be.

3. How does the number of pulleys affect the acceleration of masses in a pulley system?

The number of pulleys in a system can affect the acceleration of masses in multiple ways. Adding more pulleys can reduce the amount of force needed to lift an object, but it can also increase the distance the rope needs to travel, resulting in a longer time for the object to accelerate.

4. Can the direction of acceleration change in a pulley system?

Yes, the direction of acceleration can change in a pulley system. This is because the rope or belt can be redirected by the pulleys, causing the force to change direction and thus changing the acceleration of the masses.

5. Are there any factors other than mass and force that can affect the acceleration of masses in a pulley system?

Other factors that can affect the acceleration of masses in a pulley system include friction, the weight of the pulleys, and the type of material used for the rope or belt. These factors can influence the amount of force needed and the efficiency of the system.

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