Calculating Acceleration and Tension in a Pulley System with Inclined Planes

In summary, the block X slides up the incline (35.7 degrees above the horizontal) with positive acceleration. The magnitude of the acceleration is 0.273m/s2.
  • #1
emma3001
42
0
Please help me because my teacher has not explained how to do questions involving angles.

Blocks X and Y of masses mx=5.12kg and my=3.22kg are connected by a fishing line passing over a frictionless pulley. Show that block X slides up the incline (35.7 degrees above the horizontal) with positive acceleration. Determine the magnitude of the acceleration. (0.273m/s2 is the answer)

i want to find the gravitational force for mass x so Fg=5.12x9.8=50.2N
For mass y f=mg =3.22x9.8=31.6N

Just like with projectile problems you need to find the x and y components of Ftension for block x,which is getting pulled up at an angle but how do i do that if i don't know the applied force?
 
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  • #2
So the block y is hanging vertically?

Write the [tex]\Sigma F=ma[/tex] equation for the block y, and the [tex]\Sigma F=ma[/tex] equations for block x

Call the tension T. The acceleration of block y downward equals the acceleration of block x up the plane. Call this a.

Is the incline frictionless?

You have 2 unknowns T and a which you should be able to solve for with the equations you get.
 
  • #3
yes, the incline is frictionless and block y is hanging vertically. if i know that the normal force of y is 31.6N, does that help me in any way?
 
  • #4
emma3001 said:
yes, the incline is frictionless and block y is hanging vertically. if i know that the normal force of y is 31.6N, does that help me in any way?

If block y is hanging... how is there a normal force?

The way you described the problem... there are 2 forces acting on y... the weight, and tension... write the [tex]\Sigma f = ma[/tex] equation for y.
 
  • #5
oops... i guess i meant the gravitational force is 31.6N.
 
  • #6
if i only have the weight of block y how am i able to find out FT? After all, isn't FT calculated by saying

Fnet=FT-Fg

do i not have 2 variables here?
 
  • #7
emma3001 said:
if i only have the weight of block y how am i able to find out FT? After all, isn't FT calculated by saying

Fnet=FT-Fg

do i not have 2 variables here?

yes... I'll call FT, T...

Fnet = T - my*g

now... I'm going to take a as the downward acceleration... taking up as positive and down as negative:

my*(-a) = T - my*g (which has two variables, a and T)

can you come up with an equation for block x?
 
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FAQ: Calculating Acceleration and Tension in a Pulley System with Inclined Planes

What is Newton's Third Law of Motion?

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

How does Newton's Third Law apply to pulleys?

In the case of pulleys, when one end of the rope is pulled down, the other end is pulled up with an equal force. This is because the weight of the object on one side of the pulley is balanced by the weight of the object on the other side, causing the two objects to have equal and opposite forces acting on them.

What is the advantage of using pulleys in a system?

Pulleys allow for the distribution of force over a larger area, making it easier to lift heavy objects. This is because the more pulleys used in a system, the less force is needed to lift an object. Additionally, pulleys can change the direction of the force, making it more convenient for certain tasks.

Can pulleys violate Newton's Third Law?

No, pulleys cannot violate Newton's Third Law. The law states that forces always come in pairs and are equal and opposite, so the forces exerted on each end of the rope in a pulley system must always be equal and opposite. If this is not the case, the system is not in equilibrium and will be in motion.

Are there any real-life applications of pulleys and Newton's Third Law?

Yes, there are many real-life applications of pulleys and Newton's Third Law. Some examples include using pulleys in elevators to lift heavy loads, using pulleys in rock climbing to distribute weight and make it easier to climb, and using pulleys in construction to lift heavy materials. Essentially, any situation where a large force needs to be applied to lift an object can benefit from the use of pulleys and Newton's Third Law.

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