A rectangular block is moving along a frictionless path when it encounters the circular loop, as shown at right. The block passes points 1, 2, 3, 4, 1 before returning to the horizontal track. At point 3,

A rectangular block is moving along a frictionless path when it encounters the circular loop, as shown at right. The block passes points 1, 2, 3, 4, 1 before returning to the horizontal track. At point 3,

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter8: Potential Energy And Conservation Of Energy

Section: Chapter Questions

Problem 83AP: In an amusement park, a car rolls in a track as shown below. Find the speed of the car at A, B, and...

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A roller-coaster car shown in Figure P7.82 is released from rest from a height h and then moves freely with negligible friction. The roller-coaster track includes a circular loop of radius R in a vertical plane. (a) First suppose the car barely makes it around the loop; at the top of the loop, the riders are upside down and feel weightless. Find the required height h of the release point above the bottom of the loop in terms of R. (b) Now assume the release point is at or above the minimum required height. Show that the normal force on the car at the bottom of the loop exceeds the normal force at the top of the loop by six times the cars weight. The normal force on each rider follows the same rule. Such a large normal force is dangerous and very uncomfortable for the riders. Roller coasters are therefore not built with circular loops in vertical planes. Figure P5.22 (page 149) shows an actual design.
A student skates up a ramp that makes an angle 30° with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed ?0 and wants to turn around over a semi-circular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity) a) v02 - 2gh = (1/2) gR b) v02 - 2gh = (√3/2) gR c) the centripetal force required at points x and z is zero d) the centripetal force required is maximum at points x and z
A small block of mass 0.15 kg is placed at point A at a height 2.0 m above the bottom of a track, as shown in the figure above, and is released from rest. It slides with negligible friction down the track, around the inside of the loop of radius 0.60 m, and leaves the track at point C at a height 0.50 m above the bottom of the track. Calculate the speed of the block when it leaves the track at point C. To the best of your ability, draw and label the forces (not components) that act on the block when it is at the top of the loop at point B. Centripetal force, which is the force of an object going in a circular motion, is defined as F Centripetal = m*a = m*v2/r where “r” is the radius of the circular motion. Given this information, Calculate the minimum speed the block can have at point B without losing contact with the track. Hint: think about how the normal force will be affected! Calculate the minimum height hmin at the start of the track at which the block can be…
A small block of mass 0.15 kg is placed at point A at a height 2.0 m above the bottom of a track, as shown in the figure above, and is released from rest. It slides with negligible friction down the track, around the inside of the loop of radius 0.60 m, and leaves the track at point C at a height 0.50 m above the bottom of the track. Calculate the minimum height hmin at the start of the track at which the block can be released and still go around the loop without losing contact with the track.
A car in an amusement park ride rolls without friction around the track shown. It starts from rest at point A (it's location in the picture) at a height h above the bottom of the loop. Treat the car as a particle. a) What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B, which B being the top of the loop)? b) If h = 3.50 R and R = 20.0 m, compute the speed, radial acceleration, and tangential acceleration of the passengers when the car is at point C (labeled), which is at the end of a horizontal diameter of the loop. Show these acceleration components in a diagram, approximately to scale.
A 0.50 kg mass can slide along the frictioneless loop the loop with loop radius R = 12 cm. The block is released from rest at point P, at height h=7R above the bottom of the loop. How much work is exerted on the block by the gravitational force as it travels from P to Q? Use g = 10 N/kg.
A roller-coaster car may be represented by a block of mass 40.0 kg. The car is releasedfrom rest at a height h = 50.0 m above the ground and slides along a frictionless track.The car encounters a loop of radius R = 20.0 m at ground level, as shown in the figurebelow. As you will learn in the course of this problem, the initial height 50.0 m is greatenough so that the car never loses contact with the track.a) Find the speed of the car at the top of the loop.b) Find the minimum initial height hmin at which the car can be released that stillallows the car to stay in contact with the track at the top of the loop.
Consider a ball of mass m attached to a string of length L, which is being spun around in a horizontal circle as shown in the figure. This image is shown from above, so gravity is acting into the page. How much work is the string doing on the ball, if it moves with a constant speed v?
In the figure, a very small toy race car of mass m is released from rest,rolls down on the frictionless loop-the-loop track of radius R. It is released at a height h= 4.0 R above the floor. What is the speed of the car at point A? (point A is a point on the circle at the same height as the center of the circle but the car is on the inner side of the circle). Draw the free-body diagram of the car at point A and calculate the magnitude of the normal force that the track exerts on the car at point A? answers should be in terms of m, R, and g.
How does the centripetal force vary with the radius of a circular path? Consider constant frequency and constant speed. If centripetal force on an object is uniforms circular motion is increased, what is the effect on the frequency of rotation f ( with r constant) AND f and r when both are free to vary? Does the centripetal force acting on an object in uniform circular motion do work on the object? Explain.
A 9.72-kg ball swings rapidly in a complete vertical circle of radius 3.88 m by a light string that is fixed at one end. The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball. As the ball swings from its lowest point to its highest point, how much work is done by gravity? Give your answer in Joules to three significant figures.
A mass m moves along a frictionless track that has a loop of radius R as shown. The mass is released from such a height that it willstay on the track to make a complete circle. Find the ratio of the speed at the bottom of the track to the speed at the top of thetrack. Your answer will be a number. Please show the full work.