6. In this problem and the next, you will consider a cart rolling down a tilted board.
The cart is released from rest at the top of the board, and then rolls down the full
length of the 2 m board. The angle between the board and the table is 10°, as
shown below.
10°
We saw earlier that the component of the gravity force acting down the plane is
$mg \sin(10^\circ)$. Given this, calculate the acceleration down the board, and from
there, the velocity at the end of the board using the techniques of Unit IV.2.
7. Now, solve the previous problem again using conservation of energy and U =
mgh for the gravitational force. First, solve for the vertical distance traveled in
the 2 m down the board, and from there use conservation of energy to get the
velocity at the bottom. You should get the same answer as you got in the
previous problem!