A 1 kg object is subjected to two forces, F1 = 7 N i - 15 N j and F2 = 12 N i -
ID: 2278465 • Letter: A
Question
A 1 kg object is subjected to two forces, F1 = 7 N i - 15 N j and F2 = 12 N i - 8 N j. The object is at rest at the origin at time t = 0. What is the object's acceleration? What is its velocity at time t = 12 s? Where is the object at time t = 12 s? A 18.4 - kg box rests on a frictionless ramp with a 15.7 degree slope. The mover pulls on a rope attached to the box to pull it up the incline. If the rope makes an angle of43.2 degree with the horizontal, what is the smallest force F the mover will have to exert to move the box up the ramp?Explanation / Answer
Fx = F1x + F2x = 7 + 12 = 19 N
Fy = F1y + F2y = -15-8 = -23 N
a) ax = F1x/m = 19 m/s^2
ay = -23 m/s^2
a = (19 i - 23 j) m/s^2
b)
vx = vox + ax*t = 0 + 19*12 = 228 m/s
vy = voy + ay*t = 0 - 23*12 = -276 m/s
v = (228 i - 276 j )m/s
c)
x = 0.5*ax*t^2 = 0.5*19*12^2 = 1368 m
y = 0.5*ay*t^2 = -0.5*23*12^2 = -1656 m
r = ( 1368 i - 1656 j ) m
2) F*cos(43.2 - 15.7) = m*g*sin(15.7)
F = 18.4*9.8*sin(15.7)/cos(27.5)
= 55 N
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