**1. The problem statement, all variables and given/known data**
What horizontal force must be applied to the cart (of mass M) shown in Figure P5.67 so that the blocks remain stationary relative to the cart? Assume all surfaces, wheels, and pulley are frictionless. Notice that the force exerted by the string accelerates m(1).

Figure P5.67:

**2. Relevant equations**
Sum of forces on m(1):

1) T = m(1)*a

2) m(2)*g - T = m(2)*a

3) a = F / [M + m(1) + m(2)]

**3. The attempt at a solution**
Well, I first created the above equations. I substituted T (from equation 1) into 2), which gave me:

a = [m(2)*g] / [m(1) + m(2)]

I then subbed this into equation 3, which gave me:

F = m(2)*g*[M+m(1)+m(2)] / [m(1) + m(2)]

The book's answer is nearly the same thing, except that it's only m(1) in the denominator:

F = m(2)*g*[M+m(1)+m(2)] / m(1)

Thanks in advance for the help :)

Best,

Taylor