Answer :
Answer:
(a) m1/m2 = 1/3
(b) a = 0.75m/s^2
Explanation:
You have the following relations:
For an object of mass m1:
[tex]F_1=m_1a_1=m_1(3.00m/s^2)[/tex] (1)
For an object of mass m2:
[tex]F_2=m_2a_2=m_2(1.00m/s^2)[/tex] (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):
[tex]\frac{F_1}{F_2}=\frac{F}{F}=1=\frac{m_1(3.00m/s^2)}{m_2(1.00m/s^2)}\\\\1=3.00\frac{m_1}{m_2}\\\\\frac{m_1}{m_2}=\frac{1}{3}[/tex]
The quotient m1/m2 = 1/3
(b) For the case of a mass of m1+m2, you have:
[tex]F=(m_1+m_2)a[/tex] (3)
To find the values of the acceleration you divide the previous equation into the equation (2):
[tex]\frac{F}{F}=1=\frac{(m_1+m_2)a}{m_2(1.00)}\\\\1=\frac{m_1}{m_2}a+\frac{m_2}{m_2}a=\frac{1}{3}a+a\\\\1=\frac{4}{3}a\\\\a=\frac{3}{4}[/tex]
The new acceleratio for an object of mass m1+m2 is 3/4m/s^2 = 0.75m/s^2