Question

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?

Answer 1

a=
`5.54m/s^(2)`

Step-by-step explanation:

The net force,
`F_(net)` of the box is expressed as a product of acceleration and mass hence

`F_(net)=ma` where m is mass and a is acceleration

Making a the subject, a=
`\frac {F_(net)}{m}`

From the attached sketch,

∑
`F_(net)=Fcos\theta-F_(f)` where
`F_(f)` is frictional force and
`\theta` is horizontal angle

Substituting ∑
`F_(net)` as
`F_(net)` in the equation where we made a the subject

a=
`\frac {Fcos\theta-F_(f)}{m}`

Since we’re given the value of F as 240N,
`F_(f)` as 41.5N,
`\theta` as
`30^(o)` and mass m as 30kg

a=
`\frac {240cos30-41.5}{30.0}=\frac {166.346}{30.0}=5.54m/s^(2)`