Find the horizontal acceleration of the block?

Question

Two forces, and , act on the 7.00-kg block shown in the drawing. The magnitudes of the forces are F1=46.0 N and F2=21.0 N. Take the positive direction to be to the right

 Force F1 at angle 70o with horizontal.

Answer 1

Mass of the block,m=7 kg

Weight of the block,W=mg

                                       =(7)(9.81)

                                       =68.67 N

Horizontal component of the force F1 is

(F1)x=F1cos45=46cos45=32.53 N

Vertical component of the force F1 is

(F1)y=-F1sin45=-46sin45=-32.53 N

To find acceleration using D'Almbert equation,

ΣFx = max

(F1)x=max

ax=(F1)x/m

    =32.53/7

    =4.647 m/s^2

Horizontal acceleration,ax=4.647 m/s^2