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

240 cos 30 - 41.5 = 30a
240*1/2 - 41.5 = 30a
120 - 41.5 = 30a
30a = 78.5
a = 78.5/30 = 2.62 m/s^2

Answer 2

The magnitude of the acceleration of the box is about 5.54 m/s²

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Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

$\large {\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

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Given:

mass of box = m = 30.0 kg

magnitude of force = F = 240 N

direction of force =

frictional force = f = 41.5 N

Asked:

acceleration of the box = a = ?

Solution:

We will use Newton's Law of Motion to solve this problem as follows:

$\Sigma F_x = ma$

$F_x - f = ma$

$F \cos \theta - f = ma$

$240 \cos 30^o - 41.5 = 30.0a$

$120 \sqrt{3} - 41.5 = 30.0a$

$\boxed{a \approx 5.54 \texttt{ m/s}^2}$

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441
• Newton's Law of Motion: brainly.com/question/10431582
• Example of Newton's Law: brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics