Tension of a string passing over a pulley

[zcabral]

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?

 

[Doc Al]

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.

 

[Moetasim]

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.