Force = mass x acceleration
Mass will be considered in the horizontal direction
So the component of force in horizontal direction is 10 kg Sin (theta)
Putting the value in above equation we get:
F = 10 kg X Sin (20) X 3.4 m/s^2
= 10 Kg x 0.342 x 3.4 m/s^2
= 11.628 Kg-m/s^2
m = mass of lawn mower = 10 kg
a = acceleration along X-direction = 3.4 m/s²
let the applied force be "F"
from the force diagram , we see that only "F Cos20 " is acting along the horizontal direction .
hence F' = net force along x-direction = F Cos20
net force along x-direction is given as
F' = ma
F Cos20 = ma
inserting the values
F Cos20 = 10 x 3.4
F Cos20 = 34
F = 36.2 N
hence the force applied is 36.2 N
