Answer:
a= 1.59 m/s² : Magnitude of the acceleration
β = 65.22° (north of east) : Direction of the acceleration
Explanation:
Conceptual analysis
We apply Newton's second law:
∑F = m*a (Formula 1)
∑F : algebraic sum of the forces in Newton (N)
m : mass in kilograms (kg)
a : acceleration in meters over second square (m/s²)
Problem development
The acceleration is presented in the direction of the resultant force applied .
Calculation of the resultant forces (R)
[tex]R=\sqrt{(F_{N})^{2} +(F_{E})^{2} }[/tex]
[tex]R=\sqrt{(390)^{2} +(180)^{2} }[/tex]
R= 429.5 N
We apply the formula (1) to calculate the magnitude of the acceleration(a) :
∑F = m*a , m= 270 kg
R= m*a
429.5 =270*a
[tex]a=\frac{429.5}{270} \frac{m}{s^{2} }[/tex]
a= 1.59 m/s²
Calculation of the direction of the acceleration (β)
[tex]\beta = tan^{-1} (\frac{F_{N} }{F_{E}})[/tex]
[tex]\beta = tan^{-1} (\frac{390 }{180})[/tex]
β = 65.22° (north of east)
