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A can of paint with a mass of 6 kg hangs...

A can of paint with a mass of 6 kg hangs from a rope. If the can is to be pulled up to a rooftop with an acceleration of `1 m//s^(2)`, what must be the tension in the rope ?

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First draw a picture. Represent the object of interest (the can of paint) as a heavy dor, and draw the forces that act on the object as arrows connected to the dot. This is called a free-body (or force)diagram.

We have the tension force in the rope, `F_(T)` (also symbolized merely by T), which is upward, and the weight , `F_(w)`, which is downward. Calling up the positive direction, the net force is `F_(T)-F_(w)`. The second law, `F_("net")= ma`, becomes `F_(T)-F_(w)=ma`, so
`F_(T)=F_(w)+ma=mg+ma= m(g+a)=6(10+1(=66 N`
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