May you please help me with my physics?

Question

1.One 2.5 kg paint bucket is hanging by a massless cord from another 2.5 kg paint bucket, also hanging by a massless cord,


(a) If the buckets are at rest, what is the tension in each cord?
N (lower bucket)
N (upper bucket)
(b) If the two buckets are pulled upward with an acceleration of 1.50 m/s2 by the upper cord, calculate the tension in each cord.
N (lower bucket)
N (upper bucket)

2. A flower pot with a mass of 9.3kg is hanging by two wires that make an angle of 78° from the horizontal.
What is the tension on each wire? Newtons

What angle would the wires have to be at for the tension on each wire to be 93Newtons? wrong check markdegrees

After watering the plant, the angle of the wires changes to 79° and the tension was 47.5N. How much water was added to the plant? kg.

A third rope is added to the flower pot

If the angle that each rope makes with the horizontal remains 78° and the mass is still 9.3kg, what is the tension on each wire? Newtons

Answer 1

Call Tu the tension in the upper cord and Tl the tension in the lower cord.

looking at FBD of the upper
Tu-2.5*9.81-Tl=2.5*a
and the lower
Tl-2.5*9.81=2.5*a

a) for a=0
Tl=2.5*9.81
Tl=24.525 N

Tu=49.05 N

b) a=1.5
Tl=2.5*1.5+24.525
Tl=28.275 N

Tu=2.5*1.5+24.525+28.275
Tu=56.55 N

Call the tension in each wire T
sum in the vertical
2*T*sin(78)=9.3*9.81
solve for T
T=46.63

change angle so that T=93

2*93*sin(θ)=9.3*9.81
solve for θ
θ=29.373

2*47.5*sin(79)=m*9.81
solve for m
m=9.5, so 0.2 kg of water was added

The third wire took some thought.
The sum of the vertical forces is still zero
3*T*sin(78)=9.3*9.81
T=31.1 N

j


j