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.

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

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

Explanation:

Given that,

Mass of crate = 26.1 kg

Coefficient of kinetic friction = 0.347

We need to calculate the resultant force

Using figure

Put the value into the formula

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

Using formula of sum of force

Put the value into thr formula

(b). We need to calculate the direction

Using formula of the direction

Put the value into the formula

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

The direction  of the crate is 34.60°.