Question

A certain force gives object m1 an acceleration of 12.0 m/s2. The same force gives object m2 an acceleration of 3.30 m/s2. What acceleration would the force give to an object whose mass is (a) the difference between m1 and m2 and (b) the sum ofm1 andm2

Answer 1

The acceleration for an object with a difference in mass between m1 and m2 is 104.4 m/s², while the acceleration for an object with the sum of m1 and m2 as its mass is 183.6 m/s².

Step-by-step explanation:

To find the acceleration of an object with different masses, we can use the formula F = ma, where F is the force applied, m is the mass, and a is the acceleration. In this case, we know that the force gives object m1 an acceleration of 12.0 m/s² and object m2 an acceleration of 3.30 m/s².

(a) If we consider the difference between m1 and m2 as the mass of the object, we can substitute the values into the formula to find the acceleration: F = (m1 - m2) * a.
Acceleration = (12.0 kg - 3.30 kg) * 12.0 m/s²
Acceleration = 8.70 kg * 12.0 m/s²
Acceleration = 104.4 m/s²

(b) If we consider the sum of m1 and m2 as the mass of the object, we can use the same formula: F = (m1 + m2) * a.
Acceleration = (12.0 kg + 3.30 kg) * 12.0 m/s²
Acceleration = 15.3 kg * 12.0 m/s²
Acceleration = 183.6 m/s²

Answer 2

a) a = 4,552 m / s², b) a = 2,588 m / s²

Step-by-step explanation:

Newton's second law is

F = ma

a = F / m

in this case the force remains constant

indicate us

* for a mass m₁

a₁ = F/m₁

a₁ = 12, m/ s²

* for a mass m₂

a₂= 3.3 m / s²

a) acceleration

m = m₂-m₁

we substitute

a =
`(F)/(m_2 - m_1)`

1 / a =
`(m_2)/(F) - (m_1)/(F)`

let's calculate

`(1)/(a)` =
`(1)/(3.3) - (1)/(12)`

`(1)/(a)` = 0.21969

a = 4,552 m / s²

b) m = m₂ + m₁

a = F / (m₂ + m₁)

`(1)/(a) = (m_2)/(F) + (m_1)/(F)`

we substitute

`(1)/(a) = (1)/(3.3) + (1)/(12)`

a = 2,588 m / s²