4. The car of mass rolls from rest with negligible friction down the curved ramp and around the circular loop The initial height of the center of mass of the car is H. Assume the center of mass of the car is at a height equal to the diameter d of the loop when the car is at the top of the loop. (a) In terms of the given quantities and any fundamental constants, derive an equation for the speed vop at the top of the loop. (Neglect the rotational kinetic energy of the wheels). (b) The car is upside down at the top of the loop. Derive an equation for the minimum speed vmin necessary to make the loop.

4. The car of mass rolls from rest with negligible friction down the curved ramp and around the circular loop The initial height of the center of mass of the car is H. Assume the center of mass of the car is at a height equal to the diameter d of the loop when the car is at the top of the loop. (a) In terms of the given quantities and any fundamental constants, derive an equation for the speed vop at the top of the loop. (Neglect the rotational kinetic energy of the wheels). (b) The car is upside down at the top of the loop. Derive an equation for the minimum speed vmin necessary to make the loop.

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 small sphere with radius r starts to roll without sliding from a height h over an elevation passing from there to a circular surface (loop) of radius R=h/2. Assuming r<<R .determine(a) The speed of the body at the highest point of its trajectory (fall threshold) b) At what height does this occur ? take as zero of the base of the loop. *Attention the body does not reach the top of the loop* center of mass of the sphere = (2/5)mr² Bar center of mass=(1/12)ml²
3 - The distance between the centers of a motorcycle's wheels is 220 cm. The motorcycle's center of mass (including the bike rider) is 46.0 cm above the ground and is in the middle of the road between the two wheels. Assume that the mass of each wheel is smaller than the frame mass of the motorcycle. The engine only drives the rear wheel. How much horizontal acceleration does the motorcycle need for the front wheel to lift?A) 36.82 m / s2B) 23.43 m / s2C) 42.24 m / s2D) 34.65 m / s2E) 38.72 m / s2
1
Don't use chatgpt will upvote
Braving the Rotor at the Amusement Park (Circular Motion Due to Normal Force) The Rotor is an amusement park ride where people stand against the inside of a spinning cylinder, as shown below. Once the cylinder is spinning at a certain speed, the floor drops out of the bottom of the cylinder but the people do not fall out of the bottom. A conservative low estimate of the coefficient of static friction between people's clothes and the cylinder wall is 0.45. The radius of the cylinder is 2.4 m. What is the minimum number of rpm that the cylinder can have so that the people do not fall out the bottom? (answer: 29 rpm)
Triceps muscle 4.0 cm Biceps muscle m₁ = 2.5 kg - 16 cm CG -X W 38 cm M (positive) "counter-clockwise" PHYSICS Determine the force generated by the biceps in order to maintain the forearm in this static position (zero movement). mo is the mass of the book. ma is the mass of the forearm/wrist/hand segment. The appropriate moment arms are indicated. +y m, = 4.0 kg CG Wo M (negative) "clockwise" +X
Item 8 8 of 26 II Review | Constants Part A The parallel axis theorem relates Im, the moment of inertia of an object about an axis passing through its center of mass, to Ip, the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is I, = Iem + Md², where d is the perpendicular distance from the center of mass to the axis that passes through point p, and M is the mass of the object. Suppose a uniform slender rod has length L and mass m. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by Iem = mL. Find Iend, the moment of inertia of the rod with respect to a parallel axis through one end of the rod. Express Iend in terms of m and L. Use fractions rather than decimal numbers in your answer. • View Available Hint(s) {(m) (L²) Iend = Submit Previous Answers v Correct Part B Now consider a cube of mass m with edges of length a.…
A yoyo of radius R and mass M is released from rest with the string vertical and its top end fixed up a support as shown below. How fast is the center of mass of the yoyo moving when it has fallen a distance of 47 cm. Ignore the mass of the string and express your answer if m/s
A solid sphere of mass My radius R is released from a ramp that has a height "h"If the sphere rolls without sliding, in terms of g and h determine the velocity of the center of mass of the sphere at the base of the ramp. Justify your process
disc is purely rolling down an inclined plane of length ‘l’ & angle θ. What is the value of friction acting on it? Let the mass of the disc be M & radius be R. a) (Mgsinθ)/3 b) 0 c) (4Mgsinθ)/3 d) (2Mgsinθ)/3
The towline exerts a force of P-5.6 kN at the end of the 8-II-long crane boom. (Eigure 1) Figure SIZNIN 8m m ▾ Part A If 0 = 30° determine the placement of the hook at B so that this force creates a maximum moment about point O Express your answer to three significant figures and include the appropriate units. CH Value Submit Part B Request Answer What is this moment? Express your answer to three significant figures and include the appropriate units. Enter positive value if the moment is counterclockwise and negative value if the moment is clockwise. CH (Mo)max - Value Provide Feedback Submit Request Answer Units ? A Ⓒ 13 ? Units
Problem 4 An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall even when the floor is removed. The coefficient of static friction between the person and the wall is us = 0.3 and the radius of the drum is R = 2m. (a) Find wmin, the minimum angular speed at which the drum should rotate such that the person is held up even if the floor is removed. (hint: when the floor is removed, the person is held up by the static frictional force). (b) Find the linear speed of the person when the drum is rotating at the minimum angular speed you found in (a) (cC) Suppose that the drum started from rest and reached the speed you found in (a) in 120 seconds. During this time the drum had constant angular acceleration. Find the number of rotations made by the person within this time.