Tension of a string passing over a pulley

In summary, the problem involves a 2.50 kg object connected to a 7.50 kg object by a string passing over a pulley. The goal is to find the magnitude of acceleration for both objects and the tension in the string. Using Newton's 2nd law and analyzing the forces on each mass, two equations can be formed and solved to find the unknowns. The acceleration for both objects will be the same and the tension in the string can be found using the formula T=ma.
  • #1
zcabral
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Homework Statement



A 2.50 kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 7.50 kg object, as in Figure P5.24. Find the magnitude of the acceleration of the two objects and the tension in the string.

Figure P5.24:http://www.webassign.net/pse/p5-24alt.gif

acceleration of 2.50 kg object

acceleration of 7.50 kg object

tension in string

Formulas:

F=ma
T=ma

Work:

well i figured out the second part that the acceleration is 7.35. i used the formula a=F/m. F= 9.8 X 7.5. however i tried to doing the same for the first 1 and it said the answer was wrong. i did a=F/m. F=2.5x9.8=24.5/2.5=9.8 which was wrong. also for the tension i can't figure it out until i find the a for first part. then i plan to use the formula...T=2m1m2/m+m2*9.8...would that be the right forumla?
 
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  • #2
Since they are connected by a string, both masses have the same acceleration (in magnitude). Instead of plugging into a formula, apply basic principles. Analyze the forces on each mass and make use of Newton's 2nd law. You'll get two equations, which you can then solve to find the two unknowns: acceleration and tension.
 
  • #3


I would like to clarify that the formula for calculating acceleration is a=F/m, where F is the net force acting on the object and m is the mass of the object. In this scenario, the net force acting on the 2.50 kg object is the tension force in the string, which is equal to the weight of the 7.50 kg object (F=9.8*7.50=73.5 N). Therefore, the acceleration of the 2.50 kg object would be a=F/m=73.5/2.50=29.4 m/s^2.

As for the tension in the string, the formula T=ma is correct. However, the mass used in this formula should be the combined mass of both objects (2.50 kg + 7.50 kg = 10 kg). Therefore, the tension in the string would be T=ma=10*29.4=294 N.

It is important to remember that tension is a force, not an acceleration. I would also like to mention that in this scenario, the acceleration of the 7.50 kg object would be the same as the 2.50 kg object, as they are connected by the same string and experience the same net force. Therefore, the acceleration of the 7.50 kg object would also be 29.4 m/s^2.

I hope this clarifies the calculations for the acceleration and tension in this scenario. It is important to double-check the formulas and units used to ensure accurate calculations.
 

Related to Tension of a string passing over a pulley

What is tension?

Tension is a force that is transmitted through a medium, such as a string or rope, when it is pulled tight from both ends.

How is tension measured?

Tension is typically measured in units of force, such as newtons or pounds. It can also be measured indirectly by measuring the change in length or deformation of the medium under tension.

What is a pulley?

A pulley is a simple machine that consists of a wheel with a groove or rim around the outside and a rope or string that passes over it. Pulleys are often used to change the direction of a force or to lift heavy objects.

How does a pulley affect tension in a string?

When a string passes over a pulley, the tension in the string is equal on both sides of the pulley. This means that the force pulling down on one side of the string is equal to the force pulling up on the other side, resulting in a balanced tension.

What factors can affect the tension of a string passing over a pulley?

The tension of a string passing over a pulley can be affected by several factors, including the weight of the object being lifted, the angle of the string as it passes over the pulley, and any friction or resistance in the pulley system.

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