1. a) Using the equation and only the variables m and g , calculate the tension

Question

1. a) Using the equation and only the variables m and g, calculate the tension force required to accelerate the object upwards with an acceleration of twice the magnitude of the acceleration due to gravity.

b) The weight of the object does not change when the elevator is at rest on the 1st floor; however, the weight of the object does appear to change. Fully explain the reason the object appears to be {heavier or lighter}.

2. a) Calculate the acceleration required to change the tension force to only half of the weight of the object.

Explanation / Answer

1. a.) Let the tension required be T.

Then the equation for balancing the forces on the object would be

T (upwards) - mg (downwards) = ma (upwards)   

(here we just assumed a sign convention that upwards is positive and downwards is negative)

So, T - mg = ma

but we want the acceleration to be twice that of gravity. So, putting a = 2g ,

T - mg = m(2g)

T = 2mg + mg = 3mg

T = 3mg

b.) When the elevator is at rest , the tension will be equal to the weight since there is no other force to give acceleration So, then T = mg.

But previously in part a) we saw that tension T equaled 3mg which is three times its actual weight (due to upward acceleration). So, although the actual weight remaied costant (mg) throughout, the apparent weight seemed to change from 3mg to mg. So, the object appears to be lighter.

2. a.) Again, let us re-write the force balance equation

T (upwards) - mg(downwards) = ma (upwards)

(here we just assumed a sign convention that upwards is positive and downwards is negative)

So, T - mg = ma

We want tension force to be only half of the weight. So, putting T = mg/2

mg/2 - mg = ma

-mg/2 = ma

a = -g/2

this is the acceleration required to change the tension to only half of the weight of the object.

And don't worry about the negative sign. As per our assumed sign convention, it only says that the acceleration is downwards (downwards is negative !).

So, it needs to accelerate downwards at a rate of g/2 to change the tensin force to only half the weight of the object.

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