NZM.11 An unpowered roller-coaster car starts at rest at the top of a hill of height H, rolls down the hill, and then goes around a vertical loop of radius R. Determine the minimum value for H required if the car is to stay on the track at the top of the loop. (Hints: At the top of the loop, the car is upside down. If it is in contact with the track, though, the contact interaction will exert a normal force on the car perpendicular to the track and away from the track, since the normal force is a compression force. You may find it helpful to use conservation of energy here.)

NZM.11 An unpowered roller-coaster car starts at rest at the top of a hill of height H, rolls down the hill, and then goes around a vertical loop of radius R. Determine the minimum value for H required if the car is to stay on the track at the top of the loop. (Hints: At the top of the loop, the car is upside down. If it is in contact with the track, though, the contact interaction will exert a normal force on the car perpendicular to the track and away from the track, since the normal force is a compression force. You may find it helpful to use conservation of energy here.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A Purple Block about (mA = 24 kg) glides along a rail, it starts at point 1 with a height H1 = 5.40 m). (Entire rail is frictionless) and before entering a loop the (radius R = 1.80 m). Three more points 2, 3, and 4 are all marked on the sides as well as on the top of these loops. The purple block then comes out of the loop while travelling at a speed of 12 m/s. Has a t-bone collision with the blue block which is mB = 8 kg with a speed of 6 m/s before the collision happens. After the accident, purple block's speed is 5.30 m/s and is still moving in the same direction it was before the collision. (see picture) A)What kind of collision is this? For the purple block: (parts a-b)a.) speed of block have at point 1?v1 = _____ m/sb.) At point 2, speed of the block: v2 = _____ m/sthe force acting on the block not to closely to the circle:______ N, with the motion, against the motion, it is zero force acting on the block, radial to the circle:______ N, toward the center of the loop, away…
A 100 kg vehicle enters a flat circular turn of radius 5 m. It is initially traveling at 5 m/s counterclockwise. During the first 1/8 of a revolution The car speeds up at a rate of .0159 rad/s^2 a. Find the angular and tangential velocity after the 1/8 of a revolution b. Find centripetal and tangential acceleration after 1/8 of revolution c. Assuming the turn is not banked is it likely that the car could safely make this turn? d.
An object with mass m is attached to a string with initial length R, and moves on a frictionless table in a circular orbit with center C as shown in the figure. The string is also attached to the center, but its length is adjustable during the motion. The object initially moves with velocity v and angular velocity w Top View Given: m = 375g, v = x m/s, R = 50 cm If the length of the string is shortened from R to rR/2 while the mass is moving, the new period of the object will be the SI unit). rad/s (choose
A Lazy Susan (M=0.5 kg) in the shape of a disk is free to rotate about its center withoutfriction. It is initially motionless when a Texas-sized cockroach (m=10 g) starts runningCCW along the rim. The angular speed of the Lazy Susan is then 1 rad/sec. With whatspeed is the cockroach running (in the rest frame of the table, not the Lazy Susan)? Symbolically solve with the value taking radius as r
A mass m = 77 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 19.9 m and finally a flat straight section at the same height as the center of the loop (19.9 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) ) 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? m/s What height above the ground must the mass begin to make it around the loop-the-loop? m If the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? m/s If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the…
In the figure below, a solid ball rolls smoothly from rest (starting at height H = 8.3 m) until it leaves the horizontal section at the end of the track, at height h = 2.3 m. How far horizontally from point A does the ball hit the floor?
Please asap ?
A light, rigid rod is 77.0 cm long. Its top end is pivoted on a frictionless, horizontal axle. The rod hangs straight down at rest with a small, massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swings around in a full circle. What minimum speed at the bottom is required to make the ball go over the top of the circle?
Nonuniform ball. a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.48 m. The initial height of the ball is h =0.36 m. At the loop bottom, the magnitude of the normal force on the ball is 2.00Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form I = bMR2, but b is not 0.4 as it is for a ball of uniform density. Determine b.
A bowling ball, whose radius R is 11 cm and whose mass is 7.2 kg. rolls from rest down a plank whose length L is 2.1 m. the plank is inclined at an angle φ of 34 degrees to the horizontal. How fast is the ball moving when it reaches the bottom of the plank? please can you show the answer in hand written form
And don't worry about whether the passengers would actually survive the trip. They are lightweight crash test dummies. NTC A cart of mass m= 347 kg is going around a circular loop-the-loop. There is no motor. The cart moves only under the influence of gravity. Ignore friction and let g = 9.81 meters per second squared. The loop has a radius of r meters. When the cart is at the top of the loop, the normal force on the cart (exerted by the track) pushes down on the cart with a force of N = 1,330 newtons. When it is at the bottom of the loop, the cart has a speed of 30.7 meters per second. What is the radius of the loop (in units of meters)?
A solid ball of radius r begins to roll down a hemisphere with radius R. Find the angular speed of the ball at the moment it leaves the surface of the hemisphere. Obviously, r < R.