From summation and resultant of forces, the four answers are:
i. ∅ = 34 degrees
ii. M = 0.48 kg
iii. V = 37.5 m/s
iv. V = 37.5i + 0j + 0k
Given that Three forces acting on an object are
F1 = (−2.00 i + 2.00 j) N
F2 = (5.00 i − 3.00 j) N
F3 = (−45.0 i) N.
If the object experiences an acceleration of magnitude 3.75 m/s2.
i. The direction of the force will be the direction of the acceleration.
Sum of the forces = (-2 + 5 - 4.5)i + (2 - 3 + 0)j
Sum of the forces = -1.5i -j
The acceleration direction will be
tan∅ = [tex]\frac{y}{x}[/tex]
tan∅ = [tex]\frac{1}{1.5}[/tex]
∅ = [tex]tan^{-1}[/tex] (0.67)
∅ = 34 degrees (approximately)
ii. The mass of the object can be calculated from Newton's law.
Resultant force = mass x acceleration.
Resultant force = [tex]\sqrt{1.5^{2} + 1^{2} }[/tex]
Resultant force = [tex]\sqrt{3.25}[/tex]
Resultant force = 1.8N
Then,
1.8 = 3.75M
M = 1.8 / 3.75
M = 0.48 kg
iii. If the object is initially at rest, the speed of the object after 10.0 will be calculated by using first equation of motion.
V = U + at
Where U = 0
V = 0 + 3.75 x 10
V = 37.5 m/s
Therefore, the speed of the object after 10.0 is 37.5 m/s
iv. The velocity components of the object after 10.0 are
V = 37.5i + 0j + 0k
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