Question

Only two horizontal forces act on a 2.0 kg body. One force is 3.2 N, acting due east, and the other is 7.1 N, acting 38° north of west. What is the magnitude of the body's acceleration?

Answer 1

given,

mass of the body = 2 kg

force acting on east = 3.2 N

Force acting = 7.1 at 38° north of west

`\vec{F_1} = 3.2 \hat{i} N`

`\vec{F_2} = - 7.1 cos 38^0 \hat{i}+8.5 sin 38^0 \hat{j}`

=
`-5.59 \hat{i} + 5.23 \hat{j}`

`F_net = F_1 + F_2`

`F_net = 3.2 \hat{i} + -5.59 \hat{i} + 5.23 \hat{j}`

`F_net = -2.39 \hat{i} + 5.23 \hat{j}`

magnitude of F

`F = √((-2.39)^2+5.23^2)`

F = 5.75 N

`tan \theta = (5.23)/(-2.39)`

`\theta = tan^(-1)(-2.19)`

`\theta = 65.46`

`a = (F)/(m)`

`a = (5.75)/(2)`

a = 2.875 m/s²