Question

Two forces act on a 41-kg object. One force has magnitude 65 N directed 59° clockwise from the positive x-axis, and the other has a magnitude 35 N at 32° clockwise from the positive y-axis. What is the magnitude of this object's acceleration?

Answer 1

a = 1.41 m/s²

Step-by-step explanation:

Given that

mass ,m= 41 kg

F₁ = 65 N , θ = 59°

F₂ = 35 N ,θ = 32°

The component of Force F₁

F₁x= F₁cos59° i

F₁x= 65 x cos59° i = 33.47 i

F₁y= - F₁ sin 59° j

F₁y= - 65 x sin 59° j = - 55.71 j

The component of Force F₂

F₂x= F₂ sin 32° i

F₂x= 35 x sin 32° i = 18.54 i

F₂y= F₂ cos 32° j

F₂y= 35 x cos 32° j = 29.68 j

The total force F

F= 33.47 i + 18.54 i - 55.71 j + 29.68 j

F= 52.01 i - 26.03 j

The magnitude of the force F

`F=√(52.01^2+26.03 ^2)\ N`

F=58.16 N

We know that

F= m a

a= Acceleration

m=mass

58.16 = 41 x a

a = 1.41 m/s²