Question

The drawing shows a 26.1-kg crate that is initially at rest. Note that the view is one looking down on the top of the crate. Two forces, and , are applied to the crate, and it begins to move. The coefficient of kinetic friction between the crate and the floor is k = 0.347. Determine the (a) magnitude and (b) direction (relative to the x axis) of the acceleration of the crate.

Answer 1

(a). The magnitude of the acceleration of the crate is 1.44 m/s².

(b). The direction of the crate is 34.60°.

Step-by-step explanation:

Given that,

Mass of crate = 26.1 kg

Coefficient of kinetic friction = 0.347

We need to calculate the resultant force

Using figure

`F'=\sqrt{(F_(x)+F_(z))^2+F_(y)^2}`

Put the value into the formula

`F'=√((88cos(55)+54)^2+(88\sin 54)^2)`

`F'=126.4\ N`

(a). We need to calculate the acceleration of the crate

Using formula of sum of force

`\sum{F}=F'-\mu N`

`ma_(total)=F'-\mu mg`

`a_(total)=(F')/(m)-\mu g`

Put the value into thr formula

`a_(total)=(126.4)/(26.1)-0.347*9.8`

`a_(total)=1.44\ m/s^2`

(b). We need to calculate the direction

Using formula of the direction

`\theta=\tan^(-1)((F_(y))/(F_(x)+F_(z)))`

Put the value into the formula

`\theta=\tan^(-1)((88\sin55)/(88\cos55+54))`

`\theta=34.60^(\circ)`

Hence, (a). The magnitude of the acceleration of the crate is 1.44 m/s².

The direction of the crate is 34.60°.