Using Forces and Torques to solve a pulley problem

In summary, the conversation discusses two different approaches to solving a problem involving energy conservation and forces/torques. The first approach involves creating four equations with four unknowns, while the second approach uses mechanical energy conservation to find the solution with a single equation.
  • #1
kepherax
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Homework Statement
Please see image
Relevant Equations
Please see image
I am able to solve this easily using energy conservation, but I'm curious how one would go about solving this using forces and torques?

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  • #2
I see you have already make one equation with the net torque on the pulley. You can make two more equations by applying Newton's 2nd law on each of the masses. Then one more equation by the fact that the pulley rotates without slipping. So in total you ll have 4 equations with 4 unknowns (The two tensions, the (common) acceleration of the masses and the angular acceleration of the pulley).
 
  • #3
Alternatively, you can use mechanical energy conservation and get the answer with a single equation.
 

FAQ: Using Forces and Torques to solve a pulley problem

How do forces and torques affect a pulley system?

Forces and torques play a crucial role in determining the motion and equilibrium of a pulley system. The force applied to one end of the rope will be transmitted through the pulley to the other end, resulting in a change in direction and magnitude of the applied force. Torques, on the other hand, are responsible for rotating the pulley and causing a change in the rotational motion of the system.

How do I calculate the tension in a pulley system?

To calculate the tension in a pulley system, you need to consider the forces acting on each end of the rope. The tension in the rope will be equal to the force applied to one end of the rope, which is being transmitted through the pulley to the other end. Additionally, you can use the principle of torque equilibrium to calculate the tension in the rope.

What is the difference between static and dynamic equilibrium in a pulley system?

Static equilibrium occurs when all the forces and torques acting on a pulley system are balanced, resulting in no net movement or rotation. On the other hand, dynamic equilibrium occurs when the system is in motion, but the forces and torques acting on it are still balanced, resulting in a constant motion without any acceleration.

How do I determine the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system is determined by dividing the output force (the force applied to the load) by the input force (the force applied to one end of the rope). This ratio will give you the number of times the input force is multiplied to produce the output force. For example, a mechanical advantage of 4 means that the output force is four times larger than the input force.

Can a pulley system have an ideal mechanical advantage?

Yes, a pulley system can have an ideal mechanical advantage, which means that there is no friction present in the system. In an ideal system, all the input force is transferred to the output force without any loss due to friction, resulting in a mechanical advantage equal to the number of pulleys in the system. However, in real-world scenarios, friction is always present, and the mechanical advantage will be slightly lower than the ideal value.

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