Question

An object with a mass of `4 kg` is acted on by two forces. The first is `F_1= < -2 N , 4 N>` and the second is `F_2 = < 3 N, 5 N>`. What is the object's rate and direction of acceleration?

Answer 1

`a = 2.26` `"m/s"^2`

`theta = 83.7^"o"`

Explanation:

To solve this problem, we can use the equation

`veca = (SigmavecF)/m`

or in the component equations

`a_x = (SigmaF_x)/m`

`a_y = (SigmaF_y)/m`

Our components for the forces are

`F_(1x) = -2` `"N"`

`F_(2x) = 3` `"N"`

• `SigmaF_x = 1` `"N"`

`F_(1y) = 4` `"N"`

`F_(2y) = 5` `"N"`

• `SigmaF_y = 9` `"N"`

Using these two net force components, we can calculate the acceleration components using the equations above and it's mass (`4` `"kg"`):

`a_x = (1color(white)(l)"N")/(4color(white)(l)"kg") = 0.25` `"m/s"^2`

`a_y = (9color(white)(l)"N")/(4color(white)(l)"kg") = 2.25` `"m/s"^2`

The magnitude of the acceleration is thus

`a = sqrt((0.25"m"/("s"^2))^2 + (2.25"m"/("s"^2))^2) = color(red)(2.26` `color(red)("m/s"^2)`

And it's direction is

`theta = arctan((2.25"m"/("s"^2))/(0.25"m"/("s"^2))) = color(blue)(83.7^"o"`