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# Circular Motion

### Banking angle of velodrome.

A velodrome is built for use in the Olympics. The radius of curvature of the surface is 20 m. At what angle should the surface be banked for cyclists moving at 18m/s? (choose an angle so that no frictional force is needed to keep the cyclists in their circular path. Large banking angles are used in velodromes.)

### geodesic on the surface of a right circular cylinder

See attached file for full problem description. Show that the geodesic on the surface of a right circular cylinder is a segment of a helix. Notes: when it syas "show" the path, use the techniques oof calculus of variations to find an equation y = f(x), z = f(x,y) for the path, then explain how this function is the type of

### Equation of Motion and other Physics Problems

6 What is the equation of motion for the idealized model shown? 7 For the idealized system shown, what is the natural circular frequency in rad/sec, and the period of oscillation in seconds? 1 The equivalent spring constant of two parallel springs with spring constants 20 lb/in., and 50 lb/in. is: 8 A Mass-Spring-Damp

### A block suspended above the ground by a light rope wrapped around a pulley wheel, is released allowing it to rotate freely, letting the block fall to the ground. To determine the rotational speed, speed, time to reach the ground.

A 2 Kg block is suspended 5 m above the ground by a light rope wrapped around a 3 kg solid pulley wheel, as shown in figure. The pulley wheel, which was initially at rest, is then released allowing it to rotate freely, letting the block fall to the ground. Ignoring friction effects the rope mass: (a) Briefly state where, a

### Time taken by the wave on a stretched string.

A 15.0 kg ball is being whirled in a circular path on the end of a string. The motion occurs on a frictionless, horizontal table. The angular speed of the ball is w= 12.0 rad/s. The string has a mass of 0.0230 kg. How much time does it take for a wave on the string to travel from the center of the circle to the ball?

### Helical Wire : Mass, Center of Mass and Moment of Inertia

Consider a wire in the shape of a helix with constant density function . A. Determine the mass of the wire: B. Determine the coordinates of the center of mass: ( , , ) C. Determine the moment of inertia about the z-axis: Note: If a wire with linear density lies along a space curve , its moment of inertia about th

### Physics of Ski Jump

A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing (attached) illustrates. The crest of the second hill is circular, with a radius of r=36 m. Neglect friction and air resistance. What must be the height H of the first hill so that the skier just loses contract with

### Motion and Wedge Reaction

A particle of mass m slides down a smooth circular wedge (radius = R) of mass M (see fig). The wedge rests on a smooth horizontal table. a) Find the equation of motion of m and M b) The reaction of the wedge on m See attached file for full problem description.

### Lagrangian Dynamics.

A circle of radius R, oriented with the plane of the circle horizontal, is attached to a vertical axis at one point on the circumference of the circle. A bead, of mass m, is attached to the circle and is free to move around the circle, with no frictional losses. The circle - bead system rotates about the axis at a constant

### In a skating stunt known as the "crack the whip"

In a skating stunt known as the "crack the whip", a number of skaters hold hands and form a straight line. They try to skate so that the line rotates about the skater at one end, who acts as the pivot. The skater farthest out has a mass of 80.0 kg and is 6.10 m from the pivot. He is skating at a speed of 6.80 m/s. What is the ma

### Magnetic fields- Solar wind

The solar wind is a thin, hot gas given off by the sun. Charged particles in this gas enter the magnetic field of the earth and can experience a magnetic force. Suppose a charged particle traveling with a speed of 9.0 X 10^6 m/s encounters the earth's magnetic field at an altitude where the field has a magnitude of 1.2 X 10^-7T.

### Wave motion and equation of waves.

A plane progressive harmonic wave is represented by the equation (see attached) where is the displacement in meters, t is the time in seconds and x is distance from a fixed origin in meters. Determine the following wave properties, and where appropriate give units: a) The amplitude b) The direction of wave travel c) Th

### Simple harmonic motion

Please see the attached files for full description. 15. The displacement of a mass oscillating on a spring is given by x(t) = x_m * cos(wt + ph). If the initial displacement is zero and the initial velocity is in negative x direction, then the phase constant phi is: 16. Mass m, oscillating on the end of a spring with sprin

A race track curve has a radius of 100 meters and is banked at an angle of 68 degrees. For what speed was the curve designed? Show final answer in m/s.

### Motion of simple pendulum

The diagram shows a simple pendulum consisting of a mass M = 1.25 kg suspended by a thin string with a length of l = 0.910 m. The mass swings back and forth between ±q0. T is the magnitude of the tension in the string. 1) True or false T depends only on q. {q is for theta} The vertical component of tension is constant

### Rotational or Angular Simple Harmonic Motion

Your boss at the Cut-Rate Cuckoo Clock Company asks you what would happen to the frequency of the angular SHM of the balance wheel if it had the same density and the same coil spring (thus the same torsion constant), but all the balance wheel dimensions were made one-third as great to save material. 1) By what factor would th

### Motion on a vertical circle.

This problem is a three-parter. Here we go: A stunt man whose mass is 72.7 kg swings from the end of a 4.51 m long rope along the arc of a vertical circle. 1.) Assuming he starts from rest when the rope is horizontal, find the tension in the rope that is required to make him follow his circular path at the beginning of hi

### Derive from first principles the Poiseuille equation for pressure drop generated

Derive from first principles the Poiseuille equation for pressure drop generated by the steady flow of a Newtonian fluid through a straight tube of circular cross-section. If the flow is laminar, what is the form of the velocity profile with in the tube? Show that the mean velocity is half the peak in such circumstances.

### Centripetal Force: Car Taking an Unbanked Circular Turn

Car taking an un-banked circular turn: A car is safely negotiating an un-banked circular turn at a speed of 21m/s. The max static frictional force acts on the tires. Suddenly a wet patch in the road reduces the maximum static frictional force by a factor of three. If the car is to continue safely around the curve, to what spe

### Circular motion, one problem

A 102-gram airplane is attached to a string with a length of 1.0 meters. if it flies in a circle in which the string is declined at angle (theta) of 39.8 degrees below the horizontal at what speed is the plane flying?

### Roller Coaster: Maximum speed, forces.

(See attached file for full problem description) 1. A roller coaster ride at an amusement park lifts a car of mass 700kg to point A at a height of 90 m above the lowest point on the track, as shown above. The car starts from rest at point A, rolls with negligible friction down the incline and follows the track around a loop o

### Constant Speed of a Small Remote Car

A small remote-control car with a mass of 1.60 kg moves at a constant speed of v=12.0 m/s in a vertical circle inside a hollow metal cylinder that has a radius of 5.00m (Fig. 5-69). What is the magnitude of the normal force exerted on the car by the walls of the cylinder at a) point A (at the bottom of the vertical circle)? b) p

### A small block rests on a frictionless horizontal tabletop: What must v be if the large block is to remain motionless when released?

See attached file for full problem description with diagram. 5-102. A small block with mass m rests on a frictionless horizontal tabletop a distance r from a hole in the center of the table (Fig. 5-66). A string tied to the small block passes down through the hole, and a larger block with mass M is suspended from the free end

### Newton's Law of Motion: Two skaters are in the exact center of a circular frozen pond

Two skaters are in the exact center of a circular frozen pond. Skater 1 pushes skater 2 off with a force of 100 N for 1.69 seconds. If skater 1 has a mass of 34 kg and skater 2 has a mass of 72 kg, what is the relative velocity (v1 - v2) after the push to the nearest hundredth of a m/s? After reaching the other shore, how fas

### Four problems about tension and circular motion

(See attached file for full problem description) --- 1. In a tug-of-war, each man on a 5-man team pulls with an average force of 500 N. What is the tension in the center of the rope? A zero newtons B 100 N C 500 N D 2500 N E 5000 N 2. A ball moves with a constant speed of 4 m/s around a circle

### Forces Newton's laws of motion and dynamics of uniform circular motion for crate sliding down a ramp and car negotiating a curve

A crate is resting on a ramp that is inclined at an angle above the horizontal. As it increased, the crate remains in place until it reaches a value of 29.2°. Then the crate begins to slide down the slope. (a) Determine the coefficient of static friction between the crate and the ramp surface. (b) The coefficient of kinet

### Uniform circular motion and simple harmonic motion: Amplitude and period of this motion

An object executing simple harmonic motion has a maximum speed of 4.3 m/s and a maximum acceleration of 0.65 m/s^2. Find (a) the amplitude and (b) the period of this motion.

### Simple Harmonic Motion: During one complete cycle, for what length of time is the postion of the object greater than A/2?

An object moves with simple harmonic motion of period T and amplitude A. During one complete cycle, for what length of time is the postion of the object greater than A/2?

### The Solution to Kepler's Laws and Earth Satellites

A geosynchronous satellite stays above the same point on the equator of the Earth (a typical TV satellite). Determine algebraically: (a) The height above the Earth's surface it must be. (b) What the satellite orbital speed is?

### What is the tension in the rope at the lowest part of his path? When he reaches the highest point, what angle does the rope make with the vertical?

A kid swings from a rope 8.5 m long on a stationary pole on a playground. His body mass is 70 kg and he is moving 6.0 m/s when he passes through the lowest part of his path. What is the tension in the rope at the lowest part of his path? When he reaches the highest point, what angle does the rope make with the vertical?