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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?

User Dydil
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1 Answer

1 vote

Answer:

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)

You want to move a heavy box with mass 30.0 kg across a carpeted floor. You pull hard-example-1
User Fhchl
by
7.1k points