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A 7.0-kg object is acted on by two forces. One of the forces is 10.0 n acting toward the east. Which of the following forces is the other force if the acceleration of the object is 1.0 m/s2 toward the east?

Respuesta :

skyluke89

Answer:

3.0 N acting towards the west

Explanation:

The choices are missing, but we can find the other force by applying Newton's second law:

[tex]\sum F = ma[/tex]

where

[tex]\sum F[/tex] is the net force acting on the object

m is the mass of the object

a is the acceleration

Applied to this question, the equation becomes

[tex]F_1 + F_2 = ma[/tex]

where

[tex]F_1 = 10.0 N[/tex] is the first force (we choose east as positive direction)

[tex]F_2[/tex] is the unknown force

m = 7.0 kg is the mass of the object

[tex]a=1.0 m/s^2[/tex] is the acceleration (towards the east)

Solving for [tex]F_2[/tex],

[tex]F_2 = ma-F_1 = (7.0)(1.0)-10.0=-3.0 N[/tex]

And the negative sign means that the direction of this force is west.

johanrusli

Magnitude of the other force is 3.0 N.

Direction of the other force is west.

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Further explanation

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration (m / s²)v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

Given:

mass of the object = m = 7.0 kg

magnitude of force 1 = F₁ = 10.0 N

acceleration of the object = a = 1.0 m/s²

Unknown:

magnitude of force 2 = F₂ = ?

Solution:

Assume that the positive x-axis points East and the positive y-axis points North.

We will solve this problem by using Newton's Law of Motion as follows:

[tex]\Sigma F = ma[/tex]

[tex]F_1 + F_2 = ma[/tex]

[tex]10.0 + F_2 = 7.0(1.0)[/tex]

[tex]10.0 + F_2 = 7[/tex]

[tex]F_2 = 7.0 - 10.0[/tex]

[tex]F_2 = - 3.0 \texttt{ N}[/tex]

[tex]\texttt{ }[/tex]

Conclusion :

Magnitude of the other force is 3.0 N.

Direction of the other force is west.

[tex]\texttt{ }[/tex]

Learn more

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  • Gravity : https://brainly.com/question/1724648

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

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