Suppose that a box is accelerating at a rate of 4 m/s2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the box?
Question
Question
Suppose that a box is accelerating at a rate of 4 m/s2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the box?
Answer: 6m/s2
Explanation: Recall, F =ma
a =F/m
Where a = 4m/s2
So, 4 =F/m ………….. equation ( 1)
Now we shall see the value of a where 3F and 2m
Thus,
a =F/m
a = 3F/2m
a =3/2 ×F/m …………… equation ( 2 )
Now, substitute equation 1 into 2
F/m = 4
a =3/2 ×4
a = 12/2
a = 6m/s2
Answer:
The new acceleration of the box = 6 m/s²
That is, 1.5 of the old acceleration.
Explanation:
Acceleration of the box = 4 m/s²
From Newton’s law, F = ma
F = 4m (eqn 1)
Then the force is tripled, that is, New force, F₁ = 3F
the mass is doubled, New mass, m₁ = 2m
This will produce new acceleration, a₁
Still consistent with Newton’s law
New force = New mass × New acceleration
F₁ = m₁ × a₁
3F = 2m × a₁
a₁ = 3F/(2m)
But from eqn 1
F = 4m
a₁ = 3(4m)/2m = 3×4/2 = 6 m/s²
Hence the new acceleration = 6 m/s²