A small cube of mass m1= 1.0 kg slides down a circular and frictionless track of radius R= 0.4 m cut into a large block of mass m2= 4.0 kg as shown in the figure below. The large block rests on a horizontal and frictionless table. The cube and the block are initially at rest, and the cube m1 starts from the top of the path. Find the speed of the cube v1 as it leaves the block. Take g= 10.0 m/s2. Enter your answer in m/s.

v1=

Looks like 8:01 to me.

Well remember the work energy theorem

First m1 has potencial energy mgR then it starts moving such as the block
m1gR=1/2m1v(square2) + 1/2m2v(square2)

Remember conservation of momentum. If the cube moves one way, the large block moves the other way. There is no friction.

I was trying in this way - one equation is conservation of momentum, m2*v2 - m1*v1, and second conservation of energy, which is writen by Daoine. Two equations with two unknowns, but it gave me wrong answer

m2*v2 - m1*v1 = 0 , correction

Got it, I have been messed up with indexes

anonymous please elaborate how did u do it

you need to use conservation of momentum and conservation of energy.....

v = 2,......

i got the green tick so here is the solution

equation (1)
m1gR=0,5m1v1^2+0,5m2v2^2

m2v2-m1v1=0 so

equation (2)
v2=m1v1/m2

we substitute to equation (1)

m1gR=0,5m1v1^2+0,5m2(m1v1/m2)^2

and we solve for v1

Ps i expect a thanks ( xaxaxaxx)

Thank you so much Greco, I found a lot of help from you during this course.