Two forces act on a 4.00-kg object in a manner that the object has an accelerati
ID: 1334992 • Letter: T
Question
Two forces act on a 4.00-kg object in a manner that the object has an acceleration 3.00 m/s2 in a direction 20.0° north of east. The first force is 15.00 N in a direction 10.0° west of north. What is the second force?
A) 18.8 N in a direction 41.1° south of east
B) 12.9 N in a direction 28.1° south of east
C) 16.2 N in a direction 30.2° south of east
D) 17.5 N in a direction 37.5° south of east
E) 14.6 N in a direction 28.1° south of east
True or False
32) Force is a vector quantity.
33) A force is required for an object to move.
34) The mass of the Moon is about 1/80th of the mass of Earth. The force exerted by Earth on the Moon is about 80 times that exerted by the Moon on Earth.
35) The mass of an object is fixed, but its weight varies from location to location.
36) The gravitational force that the Sun exerts on Earth is much larger than the gravitational force that Earth exerts on the Sun.
37) The reason that when an object falls towards Earth, Earth does not move toward the object, is that the force exerted by Earth on the object is so much bigger.
Explanation / Answer
The acceleration is,
a = F2+F1/m
Hence, the second force is,
F2 = ma - F1
= 4*(3cos20i + 3sin20j) - [15(sin100o i +cos100oj)]
= 13.88 i - 10.67j
Magnitude: F2 = sqrt[13.88*13.88 + 10.67*10.67] = 17.5 N
Direction: theta = tan-1[-10.67 / 13.88] = -37.5o = 37.5o , south of east
Answer: option D
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