Calculate Tension of 6-kg Bucket of Water Pulled by String

[quicknote]

A 6-kg bucket of water is being pulled straight up by a string. The upward acceleration of the bucket is constant, with magnitude 3 {m/s^2}.

The tension in the rope is then

a about 42 N
b about 60 N
c about 78 N
d increasing as the speed increases

The net force F_y=(6 x 3) + (6 x 9.8) = 76.8 N so i would pick 'c' as my answer...but I'm not sure if this is right 'd' is throwing me off.


Now assume the bucket is accelerating downward, with magnitude 3 {m/s^2}.

a about 42 N
b about 60 N
c about 78 N
d decreasing as the speed increases


Would the answer to this be the same as part a?

Thanks

 

[Leong]

76.8 N is not the net force. that is the tension of the string. the net force is just 6*3 = 18 N. they are different. the net force is constant because the acceleration is constant, so the tension is constant also.

the answer for the second part is not the same. you have to use Newton 2nd law.

 

[hotvette]

Methodology is very important on problems like this. This almost never fails:

1. Construct free body diagram of the body and include all forces acting on the body (people often forget about gravity, and make sure the directions are correct)

2. Sum the forces and write the equation of motion F = ma

3. Manipulate the equations of motion to get what you want.

In this case, for 1 you want the tension in the rope, so solving (2) for T will give you an equation for T in terms of a, m, g

For 2, you have to keep in mind what constant velocity means in terms of acceleration