### Find Legrangian function and motion of particle

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A bicycle wheel consist of a rim ( radius R = 0. 40 m ) and essintially massless spokes. Soppose we mount the bycle wheel on the wall. so that the wheel is parallel to the wall. Is it free to spin around its center, but not freee to translate. A very light string is wrapped around the rim and a mass m + 0. 80 kg is attached to t

The frequency of a steam train whistle as it approaches you is 538Hz. After it passes you, its frequency is measured as 509 Hz., how fast the train moving (assume constant velocity)? Assume the speed of sound is 343m/s.

1. If a car goes around a curve at half the speed, the centripetal force on the car is... a.) twice as big. b.) four times as big. c.) half as big. d.) one-fourth as big. 2. What is the gravitational force between two trucks, each with a mass of 2.0 x 10^4 kg, that are 2.0 m apart? 3. The gravitational

An essentially massless spring is connected to the ceiling. A 5.00 g mass is attached to the spring so that the spring is 2.00 cm longer than its unstretched length. The mass is the pulled downward so that it is 20 cm below the equilibriun position and released from rest. After 10s the amplitude of oscillation has been reduce to

A 243 N sphere 0.199 m in radius rolls, without slipping, 6.06 m down a ramp that is inclined at 36.9° with the horizontal. What is the angular speed of the sphere at the bottom of the hill if it starts from rest?

A 243 N sphere 0.199 m in radius rolls, without slipping, 6.06 m down a ramp that is inclined at 36.9° with the horizontal. What is the angular speed of the sphere at the bottom of the hill if it starts from rest?

Physics questions The expression given below represents a transverse harmonic wave travelling along a string which is stretched along the horizontal x-axis. The expression yields the transverse wave displacement y in metres when x is entered in metres and the time t in seconds. For 1 mark each, answer the following q

See attached file. Noninertial reference systems Latitude and angular velocity of a bullet fired straight up

A dare devil decide to jump a canyon. Its walls are equally high and 10m apart. He takes off by driving a motor cycle up a short ramp sloped at an angle of 15 degrees. What minimum speed must he have in order to clear the canyon.

A 2.00 x 10^3 kg car rounds a circular turn of a radius 20.0 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.70, how fast can the car go without skidding?

Cliff divers at Acapulco jump into the sea from a cliff 36m high At the level of the sea a rock sticks out a horizontal distance at 6m. With what minimum horizontal velocity must the cliff divers leave the top of the cliff if they are to miss the rock?

Hi. Can someone please show me how to do the following problem: "An 11.2 g object moving to the right at 21.3 cm/s makes an elastic head-on collision with a 17.3 g object moving in the opposite direction at 31.5 cm/s. What is the velocity of the 11.2 g object after the collision? (positive is to the right)" Thank you!

See ATTACHMENT #1 for a diagram. A Chevrolet whose weight Wc= 2700 lb is moving at Vc = 40 mi/hr at 0 degrees. A Bronco whose weight Wb= 3600 lb is moving at Vb = 60 mi/hr at 270 degrees. The vehicles crash and lock together then move as a unit. a. On the diagram, (not to scale) show all the given data. b. Showing u

1. At t=0, a fly wheel has an angular velocity of 4.7 rad/s (radians per second), an angular acceleration of -0.25 rad/s^2 , and a reference line at pheta0 = 0. (a) Through what maximum angle phetamax will the reference line turn in the positive direction ? At what times t will the reference line be at (b) pheta = 1/2phetamax an

A 2 kg block slides along a friction-less tabletop at 8.0 m/s toward a second block (at rest) of 5 kg. A spring which obeys Hooke's law with a spring constant k = 850 N/m, is attached to the second block. (a) What will be the maximum compression of the spring? (b) What will be the velocities of the two blocks when the sprin

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 6.20 N is applied. A 1.200 kg particle rests on a friction-less horizontal surface and is attached to the free end of the spring. The particle is pulled horizontally so that it stretches the spring 5.00 cm and is then released from rest at t=0.

"The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed a distance of 0.139 m and the gun is fired vertically, the gun can launch a 25.1g projectile from rest to a maximum height of 24.5 m above the starting point of the projectile. Neglecting all resistive forces, deter

See attached graph. A solid door of mass M = 20kg and width l= 1m is hit at a right angle by a mud ball of mass m = .5kg, which hits the door at the edge with speed v= 10m/s and sticks. (a) What is the rotational inertia of the door about the hinges? (b) What is the angular velocity of the door after having been struck?

Refer to attachment for 9 Physics problems.

A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 4.2 m down a q = 23° incline. The sphere has a mass M = 4.1 kg and a radius R = 0.28 m. a) Of the total kinetic energy of the sphere, what fraction is translational? b) What is the translational kinetic energy of the sphere when i

1. A luge and its rider, with a total mass of 85 kg emerges from a downhill track onto a horizontal straight track with an initial speed of 37 m/s. If they stop at a constant deceleration of 2.0 m/s^2, (a) What magnitude F is required for the deceleration force, (b) what distance "d" do they travel while decelerating (c) what wo

A catapult on a cliff launches a large round rock towards a ship from a H of 33.0 m above sea level, directed at an angle above the horizontal with an unknown speed v(0). The projectile remains in flight for 6.00 seconds and travels a horizontal distance D of 169 m. Assuming that air friction can be neglected, calculate the valu

A vertical spring (ignore its mass), whose spring constant is 900 N/m, is attached to a table and is compressed 0.150m. What speed can it give to a .300-kg ball when released? How high above its original position (spring compression) will the ball fly?

See attached Word file. The pictures show cannonballs of two different masses projected upward and forward. The cannonballs are projected at various angles above the horizontal, but all are projected with the same vertical component of velocity. Which of the following statements are true about the situations depicted in t

A bullet whose mass M1= .04 kg traveling horizontallyhits a stationary block of mass M2= 2.4 kg on a horizontal surface. After the impact, the block, with embedded bullet, slides distance x= 5 meters to a stop. The coefficient of friction is f= .50 between block and surface. Find the velocity V1 of the bullet before impact.

A rigid rod with negligible mass has a length L= 2.6 m. The rod can rotate freely about a fixed pivot at one end. Attached at the other end of the rod is mass M1 = 8.4 kg, and at its center is mass M2 = 3.6 kg. The system is released from vertical at rest to rotate about the pivot. SEE ATTACHMENT #1 for a diagram showing parame

A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection?

A soccer player kicks a rock horizontally off a 40.0m high cliff into a pool of water. If the player hears the sound of the splash 3.00s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343m/s

ATTACHMENT #1 shows known parameters and vector polygon required. A light plane flies with airspeed (relative to the air) of 500 km/hr. The pilot sets out to fly to a city 800 km due north and finds that the plane must be headed 10 degrees east of north to fly in a straight line to the city. She arrives in 2.0 hours. Find