A small block with mass m = 17 kg slides on a frictionless track from some initial height through a loop-the-loop with radius R = 6.9 m and then along a flat straight section at the height R/2 above the ground. Assume the block never leaves the smooth track at any point on its path and the track is frictionless
What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track?
-
At what height above the ground must the block begin from rest to make it around the loop-the-loop?
-
It turns out that engineers who designed the loop-the-loop didn’t really know physics – when they made the ride, the initial height was only as high as the top of the loop-the- loop. To account for this honest mistake, they decided to give the block an initial velocity right at the beginning. How fast do they need to push the block at the beginning (now at a height equal to the top of the loop-the-loop) to get it around the loop-the-loop without falling off the track?
-
If the block has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat section?
-
Now, a spring with a spring constant k = 7180 N/m is used on the final flat surface to stop the block. How far does the spring compress?
-
Now, a rough patch of length L and with the coefficient of kinetic friction is μk = 0.25 is present on the final flat level (the spring is removed). What should it be its length for the block to stop right after passing it? What is the work done by friction?
Step by step
Solved in 1 steps with 6 images
