How Do Pulleys Affect Acceleration and Tension on an Inclined Plane?

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The tension in the string can be found by substituting the value for acceleration (2.5m/s²) into either equation (1) or (2) to solve for T. In summary, the masses A and B, each of 1kg, are connected by an inextensible string passing over a weightless pulley on an inclined plane at an angle of 30 degrees with the horizontal. Neglecting frictional forces, the acceleration of the masses is 2.5 m/s² and the tension in the string is 7.5N. There may be a typo in the given answer, as it should be 7.5N, not 75N.
  • #1
a150daysflood
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Question:
A weightless pulley is attached to the top of an inclined plane which makes an angle of 30degree with the horizontal.Masses A and B,each of mass 1kg,are joined by an inextensible string passing over the pulley.Neglecting frictional forces,calculate the accleration of the masses and the tension in the string.(Shows working thanks)

My working:
let m2 be mass of b,m1 be mass of a.Assuming acceleration due to gravity to be 10m/s².
m2g - T = m2a ---(1)
T - sin30m1g = m1a ---(2)
Substituting the values from the question,i have
From (1): 10-T=a ---(3)
From (2): T-5=a ---(4)
Substitute (3) into (4):
T=7.5N
Substituting T into (3),
a=2.5m/s²

Further Details
The answers given to me was 2.5m/s² for acceleration and 75N for tension.
Is the answers correct?
If yes,any clues to get 75N?
Thanks for replying.Appreciates it.
 
Last edited:
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  • #2
method looks good to me. is there a problem?
 
  • #3
I would agree with mjsd, your method looks correct. I would suggest that the given answer is a typo and should read 7.5N as you have.
 

FAQ: How Do Pulleys Affect Acceleration and Tension on an Inclined Plane?

What is an incline plane in physics?

An incline plane is a flat surface that is tilted at an angle. In physics, it is used to study the effects of gravity on objects and how forces act upon them.

How does an incline plane affect the motion of objects?

An incline plane reduces the effects of gravity on an object, allowing it to move along the surface with less force. This means that objects can move up or down the incline with less effort compared to moving on a flat surface.

What is the formula for calculating the force of an object on an incline plane?

The formula for calculating the force of an object on an incline plane is F = mgsinθ, where F is the force, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline plane.

What is the relationship between the angle of the incline plane and the force required to move an object?

The greater the angle of the incline plane, the less force is required to move an object. As the angle decreases, the force required to move the object increases.

How is an incline plane used in everyday life?

Incline planes are used in many everyday objects, such as ramps, stairs, and slides. They make it easier to move heavy objects, such as furniture or luggage, by reducing the amount of force needed to lift them. Incline planes are also used in machines, like cars and roller coasters, to help them move smoothly and efficiently.

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