What is the tension in the cylindrical wire?

In summary, tension is a force that opposes an object's movement and is measured in newtons or pounds using a tension meter or equations. The tension in a cylindrical wire is influenced by its length, diameter, material, weight, and external forces. It differs from compression, which is a pushing or squeezing force, and can affect a wire's strength, elasticity, and ability to withstand external forces.
  • #1
directdelta
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A cylindrical wire is placed over a frictionless pulley with one end of a wire connected to a 5.8 kg mass and the other to a 1.5 kg mass. If g=9.8 m/s/s, what is the tension in the wire?


I have no idea how to start on this.
 
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  • #2
Since it is not stated otherwise, assume the wire is massless. Draw a free body diagram for each mass and apply Newtons 2nd law to each of them. The tension in the wire will be uniform (massless wire) and the masses will have common magnitudes of displacement, velocity, and acceleration.
 
  • #3


The tension in the cylindrical wire can be calculated using the principles of Newton's laws of motion. In this scenario, the wire is acting as a rope or string, and thus the tension in the wire can be considered as the force transmitted through the wire. According to Newton's second law, the net force acting on an object is equal to the product of its mass and acceleration.

In this case, the 5.8 kg mass is pulling the wire downwards with a force of (5.8 kg)(9.8 m/s/s) = 56.84 N. This force is balanced by the tension in the wire, which is pulling the 1.5 kg mass upwards with the same force of 56.84 N. Therefore, the tension in the wire is also 56.84 N.

In summary, the tension in the cylindrical wire is 56.84 N, which is equal to the force exerted by the 5.8 kg mass downwards. This tension remains constant throughout the wire, as there are no external forces acting on it.
 

1. What is tension?

Tension is a force that is exerted on an object in a direction that is opposite to the direction of its movement. It is a pulling or stretching force that is applied to an object.

2. How is tension measured?

Tension is typically measured in units of newtons (N) or pounds (lbs). It can be measured using a tension meter or by using equations that take into account the length, mass, and other properties of the object in question.

3. What factors affect the tension in a cylindrical wire?

The tension in a cylindrical wire is affected by several factors, including the length, diameter, material, and weight of the wire. Other factors may include external forces acting on the wire, such as gravity or wind resistance.

4. How is tension different from compression?

Tension and compression are two opposite types of forces. While tension is a pulling or stretching force, compression is a pushing or squeezing force. Both forces can cause an object to change shape or size, but in opposite directions.

5. How does tension impact the behavior of a cylindrical wire?

Tension can impact the behavior of a cylindrical wire in various ways. It can determine the wire's strength and ability to bear weight or resist deformation. Tension can also affect the wire's elasticity, rigidity, and ability to withstand external forces.

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