How Do You Calculate Tension in a String When Accelerating Upwards?

AI Thread Summary
To calculate the tension in a string when a sphere is accelerated upwards, first determine the acceleration using the formula a = (delta V)/(delta t), which results in 1.91 m/s². The mass of the sphere is given as 1.55 kg, and the gravitational force is calculated as m*g, yielding 15.19 N. The tension in the string can then be found using the equation T = m(g + a), leading to a final tension of 177.87 N. It's important to note that the mass is directly provided and should not be recalculated. This method effectively illustrates how to derive tension in a dynamic system.
Kajayacht
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Homework Statement


A sphere of mass of 1.55 kg is accelerated upwards by a string to which the sphere is attached. Its speed increases from 2.21 m/s to 5.30 m/s in a time of 1.62 s. Calculate the tension in the string, assuming that the tension remains constant during that time.


Homework Equations


a = (delta)V/(delta)t
T = m(g + a)
m = wg


The Attempt at a Solution



a = (5.30 - 2.21)/1.62 = 1.91m/s^2
m = 1.55*9.8 = 15.19
T = 15.19(9.8 + 1.91) = 177.87 N
 
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Kajayacht said:

Homework Equations


a = (delta)V/(delta)t
T = m(g + a)
Good.
m = wg
Not good. You're thinking of w = mg.

The Attempt at a Solution



a = (5.30 - 2.21)/1.62 = 1.91m/s^2
Good.
m = 1.55*9.8 = 15.19
Not good. m = 1.55 kg (it's given!).
 

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