Answer:
a) W= 73.5 N
b) F₁ = 97.36 N
c) F₁y= 55.84 N
d) ay = 2.60 m/s²
Step-by-step explanation:
We apply Newton's second law:
∑F = m*a (Formula 1)
∑F : algebraic sum of the forces in Newton (N)
m : mass in kilograms (kg)
a : acceleration in m/s²
Look at the attached graphic
Free body diagram of the bucket
α= 35° : angle that forms F₁ with the x axis
β = 180 -155= 25° :angle that forms F₂ with the x axis
F₂= 88N
m=7.5 kg : mass of the bucket
g= 9.8 m/s² : acceleration due to gravity
a) W: weight of the bucket
W = m*g = 7.5*9.8
W= 73.5 N
b)Equation involving magnitudes of F1. Solve for F1
∑Fx = m *ax ax: acceleration in x , ax=0 ,
F₁* cosα- F₂*cosβ= 0
F₁* cos35° = F₂*cos25°
F₁ = (88*cos25°)/( cos35°)
F₁ = 97.36 N
c) F₁y : the y-component of force vector F₁
F₁y= 97.36* sin35°
F₁y= 55.84 N
d) ay : acceleration in y
∑Fy = m *ay
F₁* sinα+F₂*sinβ -W= m *ay
97.36* sin35°°+88*sin25° -73.5= 7.5 *ay
19.53 = 7.5 *ay
ay = (19.53) / (7.5)
ay = 2.60 m/s²