Find velocity of hanging block in a pulley system

In summary, a pulley system is set up with a 10 kg block on a desk connected to a 4 kg block hanging off the pulley. The system experiences friction with the desk and has a coefficient of kinetic friction of 0.20. Using the law of conservation of energy, the speed of the system can be found after the hanging block has dropped 1.5 m. The equations used for this calculation involve solving for the masses and determining the work done by friction and the changes in kinetic and gravitational potential energy.
  • #1
Twiggy92
4
0
A pulley is set up on the edge of a desk. A light string connects a 10 kg block laying on the desk to a 4 kg block hanging off the pulley. The only significant friction is with the desk, and the coefficient of kinetic friction is 0.20. Use the law of conservation of energy to find the speed of the system after the hanging block has dropped 1.5 m.



Wother = ΔKE + ΔUg + ΔUel
KE = 0.5 * m * v2
Ug = m*g*y



in both KE and Ug equations I need to use mass. Do I solve these equations for each of the masses and then add them all together to equal Wother?
 
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  • #2
You only need to solve the first equation, W is the work done by friction, and the system would gain kinetic energy but lose gravitational potential energy.
 

Related to Find velocity of hanging block in a pulley system

1. How do I determine the velocity of a hanging block in a pulley system?

The velocity of a hanging block in a pulley system can be determined by using the equation v = ωr, where v is the velocity, ω is the angular velocity, and r is the radius of the pulley. First, calculate the angular velocity by dividing the linear velocity of the pulley by its radius. Then, use this value to calculate the velocity of the hanging block.

2. What factors affect the velocity of a hanging block in a pulley system?

The velocity of a hanging block in a pulley system is affected by several factors, including the mass of the block, the tension in the rope, and the friction between the pulley and the rope. These factors can impact the angular velocity and, ultimately, the linear velocity of the block.

3. Can the velocity of a hanging block in a pulley system change over time?

Yes, the velocity of a hanging block in a pulley system can change over time. This is because the angular velocity of the pulley can change due to external forces, such as an increase or decrease in weight on the block, or changes in the tension or friction in the system. As the angular velocity changes, so does the linear velocity of the block.

4. How does the number of pulleys in a system affect the velocity of a hanging block?

The number of pulleys in a system does not directly affect the velocity of a hanging block. However, using more pulleys can reduce the amount of force needed to lift the block, making it easier to maintain a constant velocity. Additionally, using multiple pulleys can decrease the amount of friction in the system, resulting in a more efficient transfer of energy and potentially increasing the velocity of the block.

5. What is the relationship between the velocity of the hanging block and the velocity of the pulley in a pulley system?

In a simple pulley system where the rope is attached to the pulley and the block, the velocity of the hanging block is equal to the linear velocity of the pulley. This is because the rope is stretched taut and the pulley is rotating at a constant angular velocity. However, in more complex pulley systems with multiple ropes and pulleys, the relationship between the velocities may vary depending on the specific arrangement and forces acting on the system.

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