Question

1.Three masses, m1, m2, and m3, are lying on a plane without friction and are connected by a string. A force F is applied to the mass m1 so that the whole system accelerates along a straight line. What is the tension of the string T between the masses m1 and m2? What is the acceleration of the system?
2.A cylinder rolls without slipping on a horizontal plane and then up an incline. The linear speed of the cylinder at the beginning is v. What maximal height h will the cylinder reach?

Answer 1

1. the string is accelerating m2 and m3, so tension= (m2+m3)a

but a= F/(m1+m2+m3)

2. Figure the total energy of the rolling cyclinder: KE+ RE

1/2 mv^2 + 1/2 I w^2
1/2 mv^2+ 1/2 m r^2*v^2/r^2

so combine all that, then set it equal to mgh, and solve for h, the height it would up.