A mass of 17 kg is linked to a rope. the rope is pulled upward causing the mass to accelerate at 3.3 m/s^2, close to the surface of the earth. What is the tension in the rope in Newtons. Use g=10 m/s^2

Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter6: Circular Motion And Other Applications Of Newton’s Laws
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A mass of 17 kg is linked to a rope. the rope is pulled upward causing the mass to accelerate at 3.3 m/s^2, close to the surface of the earth. What is the tension in the rope in Newtons. Use g=10 m/s^2

Expert Solution
Given Data

The mass attached to the rope, m = 17 kg.

The acceleration of the mass, a = 3.3 m/s2.

Calculation

Three forces acts on the mass which are, the tension (T) on the rope, weight (mg) of the mass in the downward direction, and the normal force (ma) in the upward direction and these forces are related as:

T-ma=mg

Here, g is the acceleration due to gravity.

Rearrange the above expression for T.

T=mg+ma=m(g+a)                                                                                                                                     ......(1)

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