Two forces f1 and f2 act on a 5.00 kg object. taking f1=20.0n and f2=15.00n, find the acceleration of the object for the configurations:

a) mass m with f1 acting in the positive x direction and f2 acting perpendicular in the positive y direction

b) mass m with f1 acting in the positive x direction and f2 acting on the object at 60 degrees above the horizontal.

A) mass m with F1 acting in the positive x direction and F2 acting perpendicular in the positive y direction

m = 5.00 kg
F1=20.0N  ... x direction
F2=15.00N  ... y direction

Net force ^2 = F1^2 + F2^2 = (20N)^2 + (15n)^2 =  625N^2 =>

Net force = √625 = 25N

F = m*a => a = F/m = 25.0 N /5.00 kg = 5 m/s^2

5.00 m/s^2

b) mass m with F1 acting in the positive x direction and F2 acting on the object at 60 degrees above the horizontal.

m = 5.00 kg
F1=20.0N  ... x direction
F2=15.00N  ... 60 degress above x direction

Components of F2

F2,x = F2*cos(60) = 15N / 2 = 7.5N

F2, y = F2*sin(60) = 15N* 0.866 = 12.99 N ≈ 13 N

Total force in x = F1 + F2,x = 20.0 N + 7.5 N = 27.5 N

Total force in y = F2,y = 13.0 N

Net force^2 = (27.5N)^2 + (13.0N)^2 = 925.25 N^2 = Net force = √(925.25N^2) =

= 30.42N

a = F /m = 30.42 N / 5.00 kg = 6.08 m/s^2

6.08 m/s^2

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.