Answer:
Explanation:
We shall represent all the forces in vector form .
Force of 95 pounds
F₁ = 95cos100 i + 95sin100j
= -16.5 i +93.55 j
force of 75 pounds
F₂ = 75cos200 + 75sin200j
= -70.47 i - 25.65 j
force of 146 pounds
F₃ = 146cos300 i + 146sin300j
= 73i -126.44 j
Resultant force
R = F₁+ F₂ + F₃
= -16.5 i +93.55 j -70.47 i - 25.65 j +73i -126.44 j
= -13.97 i - 58.54 j
Magnitude of R = √ ( 13.97² + 58.54² )
= 60.18
If Ф be angle of resultant with axis
tanФ = - 58.54 / -13.97
Ф = 76.57 + 180 = 256.57 , because both x and y components are negative. So the resultant will be in third quadrant.
Apply Newton's second law to the bucket's vertical motion:
F = ma
F = net force, m = mass of the bucket, a = acceleration of the bucket
Let us choose upward force to be positive and downward force to be negative. The net force F is the difference of the tension in the rope lifting the bucket and the weight of the bucket, i.e.:
F = T - W
F = net force, T = tension, W = weight
The weight of the bucket is given by:
W = mg
W = weight, m = mass, g = gravitational acceleration
Make some substitutions:
F = T - mg
T - mg = ma
Isolate T:
T = ma + mg
T = m(a+g)
Given values:
m = 5kg, a = 3m/s², g = 9.81m/s²
Plug in and solve for T:
T = 5(3+9.81)
T = 64.05N