Question

A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.

Answer 1

Hii dear,

# Answer-
Acceleration = 2m/s^2 at angle of 36.37° with force of 8N.

## Explaination-
# Given-
m = 5 kg
F1 = 8 N
F2 = 6 N
a = ?

# Solution-
Consider, F be the resultant force,
F = √(F1^2 + F2^2 + 2F1F2cosθ)
F = √(6^2 + 8^2 + 2×6×8×cos90)
F = √(36+64)
F = √100
F = 10 N
Direction of force is given by,
tanθ = F2/F1
tanθ = 6/8
tanθ = 3/4 = 0.75
Taking inverse,
θ = 36.87°
The resultant force will make an angle of 36.37° with force F1.

Acceleration of body is given by,
a = F/m
a = 10/5
a = 2 m/s^2
Hence, accelration of the body will be 2m/s^2 at angle of 36.37° with force F1(of 8N).

Hope this is helpful...

Answer 2

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$\bold\red{hello...frd\:swigy\:here}$

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Mass of the body, m = 5 kg

The given situation can be represent as shown in attachment (please see attached file)

The resultant of two forces is given as:

R = √{(8)^2 + (-6)^2}=  √(64+36) = 10 N

θ is the angle made by R with the force of 8 N

Θ = tan^-1(-6/8) = -36.87°

The negative sign indicates that θ is in the clockwise direction with respect to the force of magnitude 8 N.

As per Newton’s second law of motion, the acceleration (a) of the body is given as:

F = ma

=> a= F/m = 10/5 = 2 m/s^2

I hope, this will help you

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