Block on an incline connected to a mass cord pulley 26˚. acceleration?

In summary, the student attempted to solve an equation for the acceleration of a block connected to another block by a cord by using the mass of both blocks and the tension in the cord. They were able to get an approximation by substituting in a known value for the tension in the cord.
  • #1
aly1201
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Homework Statement


block 1 lying on an inclined plane is connected to block 2 by a cord passing over a pulley.
the coefficient of kinetic friction between block 1 and the plane is .21 and block 1 and 2 are 2.6 kg. As block 2 moves down, determine the magnitude of the acceleration of block 1 and block 2 given θ=26˚ (in the diagram, block 2 isn't on a plane, just hanging)


Homework Equations



F=ma?
9.8sin26?


The Attempt at a Solution



we never learned this type of problem in class, but i found an equation in the back of my textbook g (m1sinθ-m2)/(m1+m2)
i'm guessing m1 and m2 are mass1 and mass2 so when i solved it i got 1.16. this problem is from an online site masteringphysics.com and eventually i guessed 1.8 and it was right, but i'd like to know how to actually do the problem. don't need to answer right away
 
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  • #2
In this problem, the tension in the cord and acceleration of m1 and m2 must be the same. Wright 2 equations, one for m1 and other for m2.
If a is the acceleration then
T-m1*g*sin(theta) - mu*m1*g*cos(theta) = m1*a
m2*g - T = M2*a
Solve for a.
 
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  • #3
There is also the friction force. And the trouble of which way it is acting.
I get a = 3.66.
Would appreciate seeing how you get the 1.8.
 
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  • #4
i really don't even know how to start, our teacher said he might show us on wednesday. he sent this email out to help us because so many people were emailing him questions.
"replace the mass 2 force with a tension in the connecting rope of 20.7N. This would be the force applied to mass 1. Using this value allows you to solve the problem without any further concern of the effect of moving mass 2 on the acceleration of mass 1. This greatly simplifies the solution of the problem."
 

FAQ: Block on an incline connected to a mass cord pulley 26˚. acceleration?

1. What is the formula for calculating the acceleration of a block on an incline connected to a mass cord pulley at a 26 degree angle?

The formula for calculating the acceleration of a block on an incline connected to a mass cord pulley at a 26 degree angle is a = (m1-m2)gsin(θ)/(m1+m2+M), where a is acceleration, m1 is the mass of the block, m2 is the mass on the other side of the pulley, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline.

2. How does the angle of the incline affect the acceleration of the block on an incline connected to a mass cord pulley?

The angle of the incline has a direct effect on the acceleration of the block. As the angle increases, the acceleration decreases and vice versa. This is because the component of the force acting on the block parallel to the incline decreases as the angle increases, resulting in a smaller acceleration.

3. What is the role of the mass of the block and the mass on the other side of the pulley in determining the acceleration of the system?

The masses on both sides of the pulley play a crucial role in determining the acceleration of the system. The acceleration is directly proportional to the difference in mass between the two sides. The greater the difference, the greater the acceleration. Additionally, the total mass of the system also affects the acceleration, as it is included in the denominator of the acceleration formula.

4. Can the acceleration of the block on an incline connected to a mass cord pulley at a 26 degree angle ever be zero?

Yes, it is possible for the acceleration to be zero in certain scenarios. If the mass on the other side of the pulley is significantly larger than the mass of the block, the acceleration may be zero. This is because the force of gravity on the larger mass will be greater, causing the system to remain in equilibrium and have no acceleration.

5. Does the acceleration of the block on an incline connected to a mass cord pulley depend on the length of the pulley's cord?

No, the acceleration of the block is not affected by the length of the pulley's cord. This is because the cord only serves as a medium for transferring the force from one mass to the other, and does not directly contribute to the acceleration of the block. The acceleration is only affected by the masses and the angle of the incline.

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