You want to move a heavy box with mass 30.0 kg across a carpeted floor. You pull hard on one of the edges of the box at an angle 30∘ above the horizontal with a force of magnitude 240 N, causing the box to move horizontally. The force of friction between the moving box and the floor has magnitude 41.5 N . What is the box's acceleration just after it begins to move?

Question

contestada

Respuesta :

opudodennis opudodennis · Answer 1 · 2019-10-24T15:14:30+02:00

Answer:

a=[tex]5.54m/s^{2}[/tex]

Explanation:

The net force, [tex]F_{net}[/tex] of the box is expressed as a product of acceleration and mass hence

[tex]F_{net}=ma[/tex] where m is mass and a is acceleration

Making a the subject, a= [tex]\frac {F_{net}}{m}[/tex]

From the attached sketch,

∑ [tex]F_{net}=Fcos\theta-F_{f}[/tex] where [tex]F_{f}[/tex] is frictional force and [tex]\theta[/tex] is horizontal angle

Substituting ∑ [tex]F_{net}[/tex] as [tex]F_{net}[/tex] in the equation where we made a the subject

a= [tex]\frac {Fcos\theta-F_{f}}{m}[/tex]

Since we’re given the value of F as 240N, [tex]F_{f}[/tex] as 41.5N, [tex]\theta[/tex] as [tex]30^{o}[/tex] and mass m as 30kg

a= [tex]\frac {240cos30-41.5}{30.0}=\frac {166.346}{30.0}=5.54m/s^{2}[/tex]