With your hand parallel to the floor and your palm upright, you lower a 3-kg book downward. If the force exerted on the book by your hand is 20 N, what is the book’s acceleration? With your hand parallel to the floor and your palm upright, you lower a 3-kg book downward. If the force exerted on the book by your hand is 20 N, what is the book’s acceleration?

For Newton's second law, the resultant of the forces acting on the book is equal to the product between the mass of the book and its acceleration:
[tex]\sum F = ma[/tex] (1)

There are only two forces acting on the book:
- its weight, directed downward: mg
- the force exerted by the hand on the book, of 20 N, directed upward

so, equation (1) becomes
[tex]mg - F = ma[/tex]
from which we can calculate the book's acceleration, a:
[tex]a= g - \frac{F}{m}= 9.81 m/s^2 - \frac{20 N}{3 kg}=3.14 m/s^2 [/tex]

Nudrat Nudrat · Answer 2 · 2019-08-26T11:23:27+02:00

The acceleration of the book when force is exerted on it is [tex]\fbox{\begin\\3.133\,{\text{m/}}{{\text{s}}^{\text{2}}}\end{minispace}}[/tex].

Further explanation:

The push and pull of any object is known as force. The interaction or opposition that changes the motion and direction of an object is called force.

Given:

The mass of the book is [tex]3\;{\text{Kg}}[/tex] .

The magnitude of force which is exerted on the book is [tex]20 N[/tex].

Concept used:

Newton’s second law of motion states that the rate of change of momentum is equal to the applied force.

[tex]F = \dfrac{{dp}}{{dt}}[/tex]

The expression for the momentum is [tex]\;p = mv[/tex].

Substitute value of momentum in the equation of force.

[tex]F = m\dfrac{{dv}}{{dt}}[/tex]

[tex]F = ma[/tex]

Rearrange the above expression for acceleration.

[tex]a = \dfrac{F}{m}[/tex]

When force is applied on the book then the acceleration due to gravity is also added to the total acceleration of the book. But acceleration due to gravity is directed in the opposite direction of the applied force.

The expression for the total acceleration of the book is given as.

[tex]{a_{\text{t}}} = g - a[/tex] …… (1)

Substitute [tex]\dfrac{F}{m}[/tex] for [tex]a[/tex] in equation (1).

[tex]\fbox{\begin\\{a_{\text{t}}} = g - \frac{F}{m}\end{minispace}}[/tex] …… (2)

Put [tex]3\,{\text{Kg}}[/tex] for [tex]m[/tex] and [tex]20\,{\text{N}}[/tex] for [tex]F[/tex] and [tex]9.8\,{\text{m/}}{{\text{s}}^{\text{2}}}[/tex] for [tex]g[/tex] in equation (1).

[tex]\begin{aligned}{a_{\text{t}}}&=9.8\,{\text{m/}}{{\text{s}}^{\text{2}}}-\frac{{20\,{\text{N}}}}{{3\,{\text{Kg}}}}\\&= 3.133\,{\text{m/}}{{\text{s}}^{\text{2}}}\\\end{aligned}[/tex]

The direction of the force exerted on the book is in the downward direction.

Second law of motion shows that the force is directly proportional to the acceleration of the body. The acceleration of the body has a inverse relation with the mass of the body.

Thus, the total acceleration on the book is [tex]\fbox{\begin\\{1.33m/s^2}\end{minispace}}[/tex].

Learn more:

1. Acceleration on the box due to friction https://brainly.com/question/7031524.

2. Force on the object https://brainly.com/question/6125929.

3. Newton's laws https://brainly.com/question/4033012

Answer Details:

Grade: College

Subject: Physics

Chapter: Force and momentum

Keywords:

Force, acceleration, carpeted floor, force, relative motion, motion, net force, oppose, 3.133m/s^2, 3Kg, 20N,momentum, rate of change, book, acceleration due to gravity, 9.8m/s^2.