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.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.24P

See similar textbooks

Similar questions

A person holds his outstretched arm at rest in a horizontal position. The mass of the arm is m and its length is 0.740 m.When the person releases his arm, allowing it to drop freely, it begins to rotate about the shoulder joint. Find (a) theinitial angular acceleration of the arm, and (b) the initial linear acceleration of the man’s hand. (Hint: In calculatingthe torque, assume the mass of the arm is concentrated at its midpoint. In calculating the angular acceleration, use themoment of inertia of a uniform rod of length L about one end; I = 13mL2.)
Let’s say I have a two-mass system attached to string. The string is massless and frictionless and it passes through narrow hole at center of table. m1 is on horizontal, frictionless surface moving about table and m2 is hanging vertically(stationary). How would I classify conservation of energy, linear momentum, and angular momentum of system. Explain corresponding conservations it has and why.
use two points: one taken at near the beginning of its descent,“initial”, and one just prior to the hanging mass reaching its lowest point, “final”, to determine themoment of inertia of the disk/plate. Note the position of the hanging mass is yh , and its velocity is vh . The moment of inertia isI forwhatever is rotating.1. Isolate the moment of inertia, algebraically from the above equation as all other variables have beenmeasured. Solve for the variable in terms of the others because there is no data so only working with variables.
Riders in an amusement park ride shaped like a Viking ship hung from a large pivot are rotated back and forth like a rigid pendulum. Sometime near the middle of the ride, the ship is momentarily motionless at the top of its circular arc. The ship then swings down under the influence of gravity. (a) Assuming negligible friction, find the speed (in m/s) of the riders at the bottom of its arc, given the system's center of mass travels in an arc having a radius of 16.0 m and the riders are near the center of mass. (Assume the top of the circular arc is when the pendulum arm is horizontal. You may need to use energy methods from the next chapter.) (b) What is the centripetal acceleration (in m/s2) at the bottom of the arc?
Find the required angular speed, ω, of an ultracentrifuge for the radial acceleration of a point 1.40 cm from the axis to equal 6.00×105 g (where g is the free-fall acceleration).Express your answer numerically in revolutions per minute.
A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with respect to each other. The masses and distances to the axis of the point particles are m1=0.1kg , r1=0.2m , m2=0.05kg , r2=0.4m , m3=0.5kg , r3=0.01m . (a) What is the moment of inertia of the system? (b) What is the rotational kinetic energy of the system?
A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. Does the disk reach thebottom of the plane before, after, or at the same time as the hoop?
A block of mass m rests on a slope, at an angle (theta_, and is attached by a string of negligible mass to a solid drum of mass M and radius R, as shown in the figure. When released, the block accelerates down the slope at rate a. a) Use the rotational form of Newton’s 2nd law (i.e. the net torque onthe system) to find the tension in the cable. b) Use Newton’s 2nd law (i.e. the net force on the system) to find thecoefficient of friction c) Using the expression found in part b) what is the acceleration of theblock if the slope is frictionless and the drum is massless?
Suppose that the coefficient of static friction ?s is large enough so that the annular disk rolls without slipping. What is the magnitude of the translational acceleration felt by the annular disk’s center of mass in the direction parallel to the slope?
A spool of mass m and radius R rests on a horizontal surface. Its momentum of inertia relative to its own axis is equal to I_o = c m R^2, where c is a constant. A thread is wound at a distance r. The spool is pulled without sliding along the line with a constant force F at an angle β with respect to the horizontal, as shown in the figure. Find (in terms of β, m, R, r, c, F,): the angular acceleration about the axis of the spool and the work done by force F as a function of time
A bug flying horizontally at 2 m/s collides and sticks to the end of a uniform stick hangingvertically from its other end. After the impact, the stick swings out to a maximum angleof 10.0° from the vertical before rotating back. If the mass of the stick is 15 times that ofthe bug, calculate the length of the stick (in m).
With a speed of v(initial), a perfectly rounded mass ball as known as “m” is moving towards the left and touches a uniform disc of mass as known as M and radius as known as R which is covered in super glue that instantly sticks whatever it touches and is pivoted about its center. Find the answers to the following questions How fast is the whole system rotating after the collision? Before coming to rest, to what angle will the system rotate?