Question

A constant force is applied to an object, causing the object to
accelerate at 8.0 m/s2. What will the acceleration be if
a. The force is doubled?
b. The object’s mass is doubled?
c. The force and the object’s mass are both doubled?

Answer 1

The acceleration of the object if

a. The force is doubled → a = 16 m/s²

b. The object’s mass is doubled → a = 4 m/s²

c. The force and the object’s mass are both doubled → a = 8 m/s²

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!

Given:

a₁ = 8 m/s²

Question A:

The force is doubled → F₂ = 2F₁

$F_1 : F_2 = ma_1 : ma_2$

$F_1 : F_2 = a_1 : a_2$

$F_1 : 2F_1 = 8 : a_2$

$1 : 2 = 8 : a_2$

$a_2 = 8 \times 2$

$\boxed {a_2 = 16 ~ m/s^2}$

Question B:

The object’s mass is doubled → m₂ = 2m₁

$F_1 : F_2 = m_1a_1 : m_2a_2$

$F_1 : F_1 = m_1a_1 : 2m_1a_2$

$1 : 1 = 1a_1 : 2a_2$

$1 : 1 = 1(8) : 2a_2$

$2a_2 = 8$

$a_2 = 8 \div 2$

$\boxed {a_2 = 4 ~ m/s^2}$

Question C:

The force and the object’s mass are both doubled → F₂ = 2F₁ , m₂ = 2m₁

$F_1 : F_2 = m_1a_1 : m_2a_2$

$F_1 : 2F_1 = m_1a_1 : 2m_1a_2$

$1 : 2 = a_1 : 2a_2$

$1 : 2 = 8 : 2a_2$

$2a_2 = 8 \times 2$

$2a_2 = 16$

$a_2 = 16 \div 2$

$\boxed {a_2 = 8 ~ m/s^2}$

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant

Answer 2

The second Newton's law can be written as:

$F = M*a$

Force equals to mass times acceleration.

Knowing this is easy to see that:

a) 16 m/s^2

b) 4 m/s^2

c) 8 m/s^2

Let's see how to solve the problem.

We know that the acceleration is equal to 8 m/s^2, then we can write:

$F/M = 8m/s^2$

a) What happens if we double the force?

We will have:

$F' = 2*F$

Then we can write:

$a' = F'/M$

$a' = 2*(F/M)$

And we know that

$F/M = 8 m/s^2$

Then we got:

$a' = 2*(F/M) = 2*(8 m/s^2) = 16m/s^2$

b) If the mass is doubled, we will have:

$M' = 2*M$

Then the new acceleration is:

$a' = F/M' = F/(2*M) = (1/2)*(F/M) = (1/2)*(8 m/s^2) = 4 m/s^2$

c) If we double both of them, we have:

$F' = 2*F$

$M' = 2*M$

then we have:

$F'/M' = (2*F)/(2*M) = F/M = 8 m/s^2$

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