A small object with mass 3.5 kg moves counterclockwise with constant speed 1.55
ID: 1369293 • Letter: A
Question
A small object with mass 3.5 kg moves counterclockwise with constant speed 1.55 rad/s in a circle of radius 2.95 m centered at the origin. It starts at the point with position vector 2.95 m. Then it undergoes an angular displacement of 8.80 rad.
(a) What is its new position vector?
(b) In what quadrant is the particle located and what angle does its position vector make with the positive x-axis?
(c) What is its velocity? m
(d) In what direction is it moving?
° from the +x direction.
(e) What is its acceleration? m/s2
(g) What total force is exerted on the object?
N
Explanation / Answer
r = 1.55
I = mr² = 3.9*3.8² = 56.3
8.8rad * 360°/2 = 504° = 360°+ 144°
(a) x = 3.5cos144
y = 3.5sin144
=> (-3.19i - 2.07j) in quadrant III (3)
(b) 3rd quadrant at 144°
(c) v = r = 2.95 * 1.55 = 4.6 m/s
(d) counter clockwise
(e) a = ²r = 1.55² * 2.95 = 7.1 m/s²
(g) F = mV²/r = 3.5*4.6²/2.95 = 25.1N
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