Motion in 2 Dimensions - Inclined Plane Pulleys

In summary, a 5kg mass is being pulled up a smooth incline at 30 degrees to the horizontal with an acceleration of 1.5ms^-2 using a string parallel to the incline. The question asks for the tension in the string. Using the equations Fnet = ma and the rules of right angled triangles (SOC CAH TOA), the incorrect answer of 16N is derived. However, taking into account the two components of weight and using a freebody diagram, the correct answer of 32.5N is obtained. The forces involved in the freebody diagram are the tension in the string and the force of gravity acting down the incline.
  • #1
TheKovac
24
0

Homework Statement


a Mess of 5kg is being hauled up a smooth invlined place at 30 degree to the horizontal with an acceleration of 1.5ms^-2 by mean of a string parallel to the incline:
a) What is tension in the string

Homework Equations


Fnet= ma
Rules of right angled triangles (SOC CAH TOA)
Any more?

The Attempt at a Solution


a)
=>Fnet = ma
Fnet = 5*1.6
Fnet = 8ms^-2
=>cos(theta)= O / H
cos60= O / 8
Tension = 16N = Wrong!
Answer = 32.5 N - How??
 
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  • #2
The weight has 2 components, one is perpendicular to the plane, the other is down the plane. The tension acts up the plane. So the resultant force up the plane is?

(Also,the component down the plane is always weight*sine of the angle of inclination. Not cos)
 
  • #3
2 Components. interesting..
That means the Perpendicular component
=> Fnet = ma
=> Fnet = 5*9.8
=> Fnet down = 49N

What next?
 
  • #4
Before you approach questions like these, you must have a great understanding of how to draw freebody diagrams. For this question, Fnet = Ft + (-Fg parallel) = ma. If you do not understand where these forces are coming from, let me know and I'll draw you the freebody diagram.
 
  • #5
Here, I attached a freebody diagram for the following question given that there is no force of friction due to the emphasis of a smooth surface and no coefficient of friction was given. Can you identify which forces are involved?
 

Attachments

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  • #6
Well I know that there are two main forces acting upon the pulley.

/|\
| Resistance Forces/ Tension
___
|___|

|
\|/ Gravity = 9.8ms Accel

These are the two I can think of, is there any more?
 

1. What is an inclined plane pulley?

An inclined plane pulley is a simple machine that consists of a flat surface (the inclined plane) and a wheel with a groove (the pulley) that is used to lift or move objects at an angle. It is often used in combination with other pulleys to create a mechanical advantage, making it easier to lift heavy objects.

2. How does an inclined plane pulley work?

An inclined plane pulley works by reducing the amount of force needed to lift an object. The inclined plane itself reduces the vertical force needed by spreading it out over a longer distance. The pulley then changes the direction of the force, allowing it to be applied horizontally instead of vertically. This reduces the amount of effort needed to lift the object.

3. What is the mechanical advantage of an inclined plane pulley?

The mechanical advantage of an inclined plane pulley is the ratio of the output force (the weight being lifted) to the input force (the force applied to the rope or string). The mechanical advantage of a single inclined plane pulley is equal to the number of supporting ropes attached to the pulley. For example, if there are two supporting ropes, the mechanical advantage is 2.

4. What are the applications of inclined plane pulleys?

Inclined plane pulleys have a wide range of applications, including lifting heavy objects such as construction materials, moving objects on an incline (such as wheelchair ramps), and even in exercise equipment. They are also commonly used in industrial settings to lift and move heavy machinery or equipment.

5. Are there any limitations to using inclined plane pulleys?

While inclined plane pulleys can make lifting and moving objects easier, there are limitations to their use. The angle of the inclined plane and the number of supporting ropes can affect the amount of mechanical advantage achieved. Additionally, friction can also reduce the efficiency of the pulley system. It is important to consider these factors when using inclined plane pulleys for specific tasks.

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