Question

Una Fuerza F Aplicada a un objeto de masa m1 produce Una Aceleracion De 3.00m/s^2 La Misma Fuerza Aplicada a un segundo objeto de masa m2 Produce una Aceleracion De 1.00m/s^2a) Cual Es El Valor de la relacion m1/m2? B) Si m1 y m2 se combinan en un objeto ¿Cual Es Su Aceleracion Bajo La Accion De La Fuerza F?

Answer 1

(a) m1/m2 = 1/3

(b) a = 0.75m/s^2

Step-by-step explanation:

You have the following relations:

For an object of mass m1:

`F_1=m_1a_1=m_1(3.00m/s^2)` (1)

For an object of mass m2:

`F_2=m_2a_2=m_2(1.00m/s^2)` (2)

(a) In order to calculate the quotient m1/m2 you use the fact that F1=F2=F.

You divide the equation (1) into the equation (2):

`(F_1)/(F_2)=(F)/(F)=1=(m_1(3.00m/s^2))/(m_2(1.00m/s^2))\\\\1=3.00(m_1)/(m_2)\\\\(m_1)/(m_2)=(1)/(3)`

The quotient m1/m2 = 1/3

(b) For the case of a mass of m1+m2, you have:

`F=(m_1+m_2)a` (3)

To find the values of the acceleration you divide the previous equation into the equation (2):

`(F)/(F)=1=((m_1+m_2)a)/(m_2(1.00))\\\\1=(m_1)/(m_2)a+(m_2)/(m_2)a=(1)/(3)a+a\\\\1=(4)/(3)a\\\\a=(3)/(4)`

The new acceleratio for an object of mass m1+m2 is 3/4m/s^2 = 0.75m/s^2