Question

two forces act on a point object as follows : 100 N at 170^o and 100 N at 50^o. Find the resultant force
a) 110 N at 50^o
b) 110 N at 100^o
c) 100 N at 110^o
d) 100N at 50^o

Answer 1

Answer on Question #48309, Physics, Mechanics | Kinematics | Dynamics

Question:

two forces act on a point object as follows : 100 N at $170^{\wedge}o$ and 100 N at $50^{\wedge}o$ . Find the resultant force

a) $110\mathrm{N}$ at $50^{\wedge}\mathrm{o}$

b) $110\mathrm{N}$ at $100^{\wedge}\mathrm{o}$

c) $100\mathrm{N}$ at $110^{\wedge}\mathrm{o}$

d) $100\mathrm{N}$ at $50^{\wedge}\mathrm{o}$

Answer:

Components of the resultant force equals:

$$F _ {x} = 1 0 0 \cos 5 0 {}^ {\circ} + 1 0 0 \cos 1 7 0 {}^ {\circ}$$ $$F _ {x} = 1 0 0 \sin 5 0 {}^ {\circ} + 1 0 0 \sin 1 7 0 {}^ {\circ}$$

The resultant force equals:

$$F = \sqrt {F _ {x} ^ {2} + F _ {y} ^ {2}} = 1 0 0 N$$

Angle equals:

$$\arctan \frac {F _ {y}}{F _ {x}} = 1 1 0 {}^ {\circ}$$

Answer: c) $100\mathrm{N}$ at $110^{\wedge}\mathrm{o}$

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