### Shortest path between two points in polar coordinates

Show that the shortest path between two given points in a plane is a straight line, using plane polar coordinates.

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Show that the shortest path between two given points in a plane is a straight line, using plane polar coordinates.

Q. Bouncing a ball: Let g be the acceleration of gravity near the Earth's surface. The acceleration of gravity near the surface of the Moon is (approximately) g/6. Using the law of conservation of energy, i.e. the principle of conservation of energy, solve the following. (a) Suppose that a ball is dropped from 9 feet above

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The first energy crisis in the U.S occurred in 1973. In response many new devices were created and many installed. Today, companies appear to be disinterested in energy conservation despite the rule of thumb that 50% of the energy expense can be saved with basic conservation devices. Why would companies not be interested in avoi

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1. If the lower layer of the liquid in the graduated cylinder is salt water, and the top half water, what conclusions can you make with respect to the density of the egg. Foe example, is the egg denser than salt water? than pure water? Why? 2. A 325gram piece of gold at 425C is dropped into 200ml of water at 22.0C. The specif

An electron is projected with an initial speed of 4.8 *10^5 m/s directly toward a proton that is fixed in place. If the electron is initially a great distance from the proton, at what distance from the proton is the speed of the electron instantaneously equal to twice the initial value?

A small steel ball is rolled down an inclined plane from a table. The inclined plane is a slotted ruler. One end of the ruler is 10cm off of the table. The ball leaves the table horizontally and lands 46cm from the table on the floor. The table is 72 cm from the ground. 1. Using projectile motion equations, determine the spee

A block of mass slides along a frictionless table with a speed of 10 m/s. Directly in front of it, and moving in the same direction, is a block of mass moving at 3.0m/s. A massless spring with spring constant is attached to the near side of (the side facing ). When the blocks collide, what is the maximum compression of th

A file is attached for the sample a mass of 0.5 kg is suspened from a spring, which stretches by 8 cm. the support from which the spring is suspended is set into siusoidal motion. with what frequency should the tip be tapped to make the strip oscillate with the maximum amplitude?

(See attached file for full problem description) 19. The graphs attached show the force acting on a particle as the particle moves along the positive x axis from the origin to x = x1. The force is parallel to the x axis and is conservative. The maximum magnitude F1 has the same value for all graphs. Rank the situations accor

39) A particle of mass m=30 g slides inside a bowl whose cross section has circular arcs at each side and a flat horizontal central portion between points a and b of length 20 cm. The curved side oft he bowl are frictionless, and for the flat bottom the coefficient of kinetic friction Mk-0.21. The particle is released from rest

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1. A 5.3 g bullet leaves the muzzle of a rifle with a speed of 336 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.92 m long barrel of the rifle? 2. A shopper in a supermarket pushes a loaded cart with a horizontal force of 12 N. The cart has a mass of 29 kg. (a) How far will i

1.) A box has three identical bulbs mounted on its top with the wires hidden inside the box. Initially bulb A is the brightest and bulbs B and C are equally bright. If you unscrew A, bulbs B and C go out. If you unscrew B, A gets dimmer and C gets brighter so that A and C are equally bright. If you unscrew C, A gets dimmer a

1) A 10.0 g moving to the right at 20.0 cm/s makes and elastic head on collision with a 15.0 g object moving in the opposite direction at 30.0 cm/s. Find the velocity of each object after collision. 2) a 90 kg fullback moving east with a speed of 5 m/s is tackled by a 95 kg opponent running north at 3.0 m/s. If the collis

The coefficient of restitution, e, for a ball hitting a stationary surface with a velocity v1 and rebounding with a velocity v2 is: e = - v2/v1 The value of e is positive, because v1 and v2 have opposite directions, and can be any number from 0 to 1 for a passive collision with the surface(no explosive type energy release

Two particles each have a mass of 5.4 x 10-2 kg. One has a charge of +4.8 x 10-6 C, and the other has a charge of -4.8 x 10-6 C. They are initially held at rest at a distance of 1.1 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-half its

(See attached file for full problem description with diagrams) --- Question 1: A 0.20-kg billiard ball traveling at a speed of 15 m/s strikes the side rail of a pool table at an angle of 60 degree. If the ball rebounds at the same speed and angle, what is the change in its momentum? Question 2: A one-dimensional impulse f

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(See attached file for full problem description)

10. A small block of mass m1 = 0.480 kg is released from rest at the top of a curved-shaped frictionless wedge of mass m2 = 3.00 kg, which sits on a frictionless horizontal surface as in Figure (see attachment). When the block leaves the wedge, its velocity is measured to be v1 = 3.60 m/s to the right, as shown in Figure. (a

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