A cart rolls with negligible friction down a ramp that is inclined at an θ=30∘θ=30∘ above level ground. It is released from rest at a height h=46h=46 cm. What we want to do is to figure out how fast the cart will go when it reaches the bottom of the ramp.
x
x
Let's begin by establishing the equations that model the motion of the cart. Recall that we are dealing here with an example of constantly accelerated motion. Let the xx axis point down the ramp and let x=0x=0 correspond to the starting position of the cart. What are the equations that describe the motion of the cart? [These should incorporate that both the initial position and velocity are zero. Use 'g' to indicate the gravitational acceleration, 'B' to indicate the angle, and 't' for the time variable. To write a function like sin(θ)sin⁡(θ) you should write `sin(B)'.]
v(t) =
x(t) =
B.) Next, we need to establish our coordinates a bit more. Let x=xbottomx=xbottom be the as-yet unknown coordinate at the bottom of the ramp. What is the value of xbottomxbottom? [Tip: Think about trigonometry, where the ground and the ramp form two sides of a right triangle.]
C.)
After reaching the bottom of the ramp, the cart smoothly slides onto another ramp, maintaining the same speed that it had at the bottom of the first ramp. The second ramp is tilted 36∘∘ above the level ground. How far up the ramp does the cart go?