Answer:
(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
[tex]F'=\sqrt{(F_{x}+F_{z})^2+F_{y}^2}[/tex]
Put the value into the formula
[tex]F'=\sqrt{(88\cos{55}+54)^2+(88\sin 54)^2}[/tex]
[tex]F'=126.4\ N[/tex]
(a). We need to calculate the acceleration of the crate
Using formula of sum of force
[tex]\sum{F}=F'-\mu N[/tex]
[tex]ma_{total}=F'-\mu mg[/tex]
[tex]a_{total}=\dfrac{F'}{m}-\mu g[/tex]
Put the value into thr formula
[tex]a_{total}=\dfrac{126.4}{26.1}-0.347\times9.8[/tex]
[tex]a_{total}=1.44\ m/s^2[/tex]
(b). We need to calculate the direction
Using formula of the direction
[tex]\theta=\tan^{-1}(\dfrac{F_{y}}{F_{x}+F_{z}})[/tex]
Put the value into the formula
[tex]\theta=\tan^{-1}(\dfrac{88\sin55}{88\cos55+54})[/tex]
[tex]\theta=34.60^{\circ}[/tex]
Hence, (a). The magnitude of the acceleration of the crate is 1.44 m/s².
The direction of the crate is 34.60°.
