Respuesta :
Answer:
mag (a) = 0.7707 m/s^2
a = - 0.62963 i - 0.4444 j
Explanation:
Given:
- Force 1 , F_1 = - 12 j
- Force 2, F_2 = - 17 i
- mass of the object m = 27 kg
Find:
What is the acceleration of the object
Solution:
- The relation between the Force vector and the acceleration vector of an object can be given by the Newton's Second Law of motion:
                  F = m*a
Where a is the acceleration vector.
                 (-17 i - 12 j ) = m*a
                 a = (-17 i - 12 j ) / 27
                 a = - 0.62963 i - 0.4444 j
- The magnitude of the acceleration mag (a) is given by:
                 mag (a) = sqrt ( (-0.62963)^ 2 + (-0.44444)^2 )
                 mag (a) = sqrt ( 433/729)
                mag (a) = 0.7707 m/s^2
Answer:
The acceleration of the object is  0.77[tex]m/s^{2}[/tex] in the negative x and y direction.
Explanation:
Given;
[tex]F_{1}[/tex] = 12N (due South)
[tex]F_{2}[/tex] = 17N (due West)
The resultant force F acting on the body is given by;
F = [tex]\sqrt{F_{1} ^{2} + F_{2} ^{2}}[/tex]
F = [tex]\sqrt{12^{2} + 17^{2}}[/tex]
F = [tex]\sqrt{144 + 289}[/tex]
F = [tex]\sqrt{433}[/tex]
F = 20.8N
This resultant force will act on the body and cause the acceleration.
Using Newton's law of motion;
F = m x a
Where;
F = resultant force = 20.8N
m = mass of the object = 27kg
=> 20.8 = 27 x a
=> a  = 20.8 / 27
=> a = 0.77[tex]m/s^{2}[/tex]
And since the forces are acting due South and due West, the direction of acceleration will be in the negative -x and -y direction.
