If the buckets are at rest what is the tension in each cord?

[needhelp83]

5. One 3.5 kg paint bucket is hanging by a massless cord from another 3.5 kg paint bucket, also hanging by a massless cord.
a) If the buckets are at rest what is the tension in each cord?
b) If the two buckets are pulled upward with an acceleration of 1.6 m/s2by the upper cord, calculate the tension in each cord.

a) Tension of Top bucket
F=ma= (3.5 kg)(9.80 N/kg) = 34.3 N

Tension of Lower bucket
F=ma= (3.5 kg)(9.80 N/kg) = 34.3 N
Total Force=68.6 N

b)
Lower Bucket
T - 34.3 N = (7.0 kg)(+1.6 m/s/s)= 45.5 N

Upper Bucket
T - 34.3 N - 45.5 N = (3.5 kg)(+1.6 m/s/s) = 85.4 N

Double checking? Look good?

 

[andrevdh]

a) Analyze each bucket separately. Draw a force diagram for each of the buckets separately (they both have the same weight, call it W). Label the tension in the upper rope T1 and the lower rope T2. Then construct the equation for each of the buckets according to Newton's second law:

$$\Sigma F_Y = ma_Y = 0$$

What do you get for the two equations?

 

[HallsofIvy]

5. One 3.5 kg paint bucket is hanging by a massless cord from another 3.5 kg paint bucket, also hanging by a massless cord.
a) If the buckets are at rest what is the tension in each cord?
b) If the two buckets are pulled upward with an acceleration of 1.6 m/s2by the upper cord, calculate the tension in each cord.

a) Tension of Top bucket
F=ma= (3.5 kg)(9.80 N/kg) = 34.3 N

Tension of Lower bucket
F=ma= (3.5 kg)(9.80 N/kg) = 34.3 N
Total Force=68.6 N

The problem did not ask for the tension in the buckets it asked for the tension in the cords. The top cord is supporting both buckets, the lower cord is supporting only the bottom bucket.

b)
Lower Bucket
T - 34.3 N = (7.0 kg)(+1.6 m/s/s)= 45.5 N

Upper Bucket
T - 34.3 N - 45.5 N = (3.5 kg)(+1.6 m/s/s) = 85.4 N

Same point as before. F= ma so add that to each- again remembering to use the mass of both buckets for the upper cord. You appear to have done that here.

Double checking? Look good?

 

[needhelp83]

Tension of Cord in Lower bucket
F=ma= (3.5 kg)(9.80 N/kg) = 34.3 N
Tension of Cord in Top bucket

F=ma= (3.5 kg)(9.80 N/kg) = 34.3 N
34.3 N + 34.3 N= 68.6 N


b)
Tension in cord from Lower Bucket
T - 34.3 N = (3.5 kg)(+1.6 m/s2)= 39.9 N

Tension in cord from Upper Bucket
T – 34.3 N - 39.9 N = (3.5 kg)(+1.6 m/s2) = 79.8 N

How about this?

 

[andrevdh]

Well done. You've got the tensions right.