Pulleys/Static equilibrium

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In summary, the problem is to find the mass of a counterweight needed to balance a 1600 kg truck on an incline, assuming frictionless and massless pulleys. The conditions for static equilibrium and the use of Newton's second law can help solve this problem.
  • #1
xdevinx
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Homework Statement



Find the mass m of the counterweight needed to balance the 1600 kg truck on the incline. Assume all pulleys are frictionless and massless.

Picture attached

Homework Equations



Conditions for static equilibrium so that angular acceleration=0:
[tex]\sum[/tex]Torque=0

The Attempt at a Solution



We're learning about rotational dynamics and torque and I honestly cannot make the connection between that and this problem. Please help ):
 

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  • #2
Welcome to PF!

xdevinx said:
Find the mass m of the counterweight needed to balance the 1600 kg truck on the incline. Assume all pulleys are frictionless and massless.

We're learning about rotational dynamics and torque and I honestly cannot make the connection between that and this problem. Please help ):

Hi xdevinx! Welcome to PF! :smile:

I can't see the diagram yet, but if this is a standard weight-pulley-weight problem, then rotational dynamics and torque and irrelevant …

just call the tension T, and use good ol' Newtons second law twice (once on each weight). :wink:
 
  • #3


I understand your confusion and I am here to help. In this problem, we are dealing with static equilibrium, which means that the truck is not moving. This means that the sum of all forces and torques acting on the truck must be equal to zero. In order for the truck to be in equilibrium, the torque due to the weight of the truck must be balanced by the torque due to the counterweight.

To find the mass of the counterweight needed, we can use the equation for torque: T = r x F, where T is the torque, r is the distance from the pivot point to the point of application of the force, and F is the force acting on the object. In this case, the pivot point is at the bottom of the incline and the force is the weight of the truck. The distance r can be calculated using trigonometry.

Once we have the torque due to the weight of the truck, we can set it equal to the torque due to the counterweight and solve for the mass m. This will ensure that the truck is in static equilibrium and will not roll down the incline.

In summary, we can use the principles of static equilibrium and torque to determine the mass of the counterweight needed to balance the truck on the incline. I hope this helps and feel free to ask any further questions if needed.
 

What is a pulley and how does it work?

A pulley is a simple machine that consists of a wheel with a groove in its rim and a rope or cable that runs along the groove. It works by changing the direction of the force applied to the rope in order to lift or move an object. When the rope is pulled down, the object attached to it is lifted up.

What are the different types of pulleys?

There are three main types of pulleys: fixed, movable, and compound. A fixed pulley is attached to a surface and changes the direction of the force. A movable pulley is attached to the object being moved and reduces the amount of force needed to lift or move the object. A compound pulley is a combination of fixed and movable pulleys, which allows for larger loads to be lifted with less force.

How does a pulley affect static equilibrium?

A pulley can affect static equilibrium by balancing the forces acting on an object. In order for an object to be in static equilibrium, the sum of all the forces acting on the object must be equal to zero. A pulley can change the direction and magnitude of the force applied to an object, which can help to balance the forces and maintain static equilibrium.

What is the mechanical advantage of a pulley?

The mechanical advantage of a pulley is the ratio of the output force to the input force. In other words, it tells us how much the force is multiplied or reduced when using a pulley. The mechanical advantage of a pulley is determined by the number of ropes supporting the object and can range from 1 (no mechanical advantage) to the number of ropes attached to the object.

How can pulleys be used in real-world applications?

Pulleys have a wide range of applications in various industries such as construction, transportation, and manufacturing. They are used in cranes and elevators to lift heavy objects, in escalators to move people, and in automobiles to control the movement of engine parts. Pulleys are also used in simple machines like bicycles and exercise equipment.

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