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# Classical Mechanics

### Steel piano string: Fundamental frequency and wavelength, speed of a wave

A steel piano string is .05m in length, with a mass of .005kg, and has a tension of 400N. 1) what is the fundamental frequency and wavelength of the string? 2) What is the speed of a wave on this string? 3) If the tension is increased to 450N, what is the new fundamental frequency?

### Motion: Calculate the minimum average speed an opponent must move to hit a lofted ball

If you loft a ball with an initial speed of 15.0 m/s at an angle of 50 degrees above the horizontal. At this instant your opponent is 10 m away from the ball. He begins moving away from you .30 sec later, hoping to reach the ball and hit it back at the moment that it is 2.10 m above its launch point. I'm trying to figure out wha

### Pressure on the ground

A woman wearing high healed shoes placed about 50% of her full weight on a single heal when walking. A) Assuming the woman weighs 530 N, what is the pressure on the ground under one heal if the area of contact per heal is 6.5 cm^2? What if this area was 1.0 cm^2? B) How does this compare with the pressure underneath an ele

### Density of a block of wood

A block of wood 10 cm x 30 cm x 5.5 cm thick has a mass of 1240 grams. A) What is the density of this wood? B) Is the wood most likely balsa, or oak?

### Momentum of Automobile

I need to see each step and formula to solve this question: The momentum of an object traveling at 5.3 m/s is determined to be 350 kg m/s. Could the moving object be an automobile?

### Given momentum and mass, find speed

A 1.73-kg physics book flies through the air with a momentum of 18.8 kg m/s. What is its speed?

### Smith chart and two wire lines

The two-wire lines shown in the attached figure are all lossless have Z0 = 200 ohms. Find d and the shortest possible value for d1 to provide a matched load if gamma = 100cm. Please show all steps using smith chart. (See attached file for full problem description)

### Measurements of Beams

Please see attachment 1) Determine the location of the centroid yc, measured from the bottom, for a beam with the cross section shown in the figure. A) 0.5 in B) 2.5 in C) 3.0 in D) 5.0 in 2) Determine the maximum flexural stress produced by a resisting moment Mr of +5000 ft*lb if the beam has the cross section sho

### Extension Length of a Circus Performer's Elastic Rope

A 56.5 kg circus performer bobs up and down at the end of a long elastic rope at a rate of once every 5.70 s. The elastic rope obeys Hooke's law. Find how much the rope is extended beyond its unloaded length when the performer hangs at rest.

### Buoyant Force on Ice

An ice cube is placed in a glass of water. The cube is 2.0 cm on each side and has a density of 0.917 g/cm3. What is the buoyant force on the ice?

### Problems of Analytical Mechanics

1.27 Prove that [v x a] = v^2/p where p is the radius of curvature of the path of a moving particle, 1.29 What is the value of x that makes the following transformation R orthogonal? What transformation is represented by R? (See attached file for full problem description)

### Calculations regarding fluids and solids

A hollow aluminum tube (diameter= 4.46 cm) is sealed at one end and loaded with lead shot to give a total mass of 0.237 kg. When the tube is floated in pure water, what is the depth, z, of its bottom end?

### A freight train mass, pull and speed problem

A freight train has a mass of 3.0 x 106 kg. If the locomotive can exert a constant pull of 6.0 x 105 N, how long does it take to increase the speed of the train to 50 km/hr?

### Train moving at constant speed when a ball is dropped

If you were riding on a train moving at constant speed along a straight track and you dropped a ball directly over a white dot on the floor, what would you see? If Jane is outside of the train standing on the ground beside the track, what would she see? Explain.

### Dynamics engineering problem

1. The balloon A is ascending at the rate of v_A=12km/h and is being carried horizontally by the wind at v_w=20km/h. If a ballast bag is dropped from the balloon at the instant h=50m, determine the time needed for it to strike the ground. Assume that the bag was released from the balloon with the same velocity as the balloon. Al

### Mixed Algebra & Calculus Problems

(See attached files for full problem descriptions) --- Problem Set 1 1) If 2x + y = 3 and x - y = 3: a) What is x? A) 1 B) 2 C) 3 D) 0 E)-1 b) What is y? A) 1 B) 2 C) 3 D) 0 E)-1 2) If you walk 3 miles in one hour and then 4 miles in two hours, what is your average speed for the entire trip? (in mph

### Energy of pulse on a string

Here is a string problem I'm having much trouble with. An explanation would be greatly appreciated. It's written much more clearly on the attachment, so please go there first!!! Here it is, Consider a string under a tension T, mass density &#961; with a pulse ξ(x,t) = ξ_0^ (-(x-ct)^2/a^2) . propag

### Maximum load of a raft

A raft is constructed of wood having density 600kg/m^3. Its surface area is 5.8m^2 has a thickness of 12 cm. Find the maximum load the raft can carry on it without sinking. (density of water 100kg/m^3)

### Fluids Cross-Sectional Area

In the hydraulic lift the red piston has a cross-sectional area of 0.69 m2 and the green piston a cross-sectional area of 0.06 m2 and the force F1 = 176 N. What weight to the nearest newton can this configuration lift? If the green piston is depressed 0.67 meters, how far up would the red piston move to the nearest thousandth

### Speed, time, distance

Bobby traveled a distance of 50x+150 miles at 50 miles per hour on the Gulf Freeway. Find a binomial that represents the time that he traveled.

### Calculating gravitational potential energy

A crate weighing 550 N is dragged 20 m up a 60 degree incline. What is the change in the gravitational potential energy of the crate?

### Calculating displacement given direction and distances

A person moves 30m north, then 20m east then 30 squareroot of 2 m 45 degrees south of west. The person's displacement from the original position is what?

### Determining units of an equation

If x = a + bt + ct^2, where x is in meters and t is in seconds, what is the unit of c?

### Mass comparison problem

Two objects have the same kinetic energy. if the first object is moving 3 times faster than the second object, what is the second object's mass in comparison to the first object's mass?

### Coordinates of the Center of Mass

The coordinates of three particles are (5, 7), (0, 3), and (-1,-1). If the three particles have masses of 1.0 kg, 2.0 kg and 2.0 kg respectively, what are the coordinates of the center of mass?

### Oscillation and Pendulum Motion

A mass on a string of unknown length oscillates as a pendulum with a period of 4.0 (s). Parts a to d are independent questions, each referring to the initial situation. What is the period if: a. The mass is doubled? in seconds b. The string length is doubled? in seconds c. The string length is halved? in seconds d. The ampli

### Classical mechanics problems

(See attached file for full problem description) Please change the file extension to *.doc so that it can be open by Word. 15. A ball of mass 0.5 kg, initially at rest, acquires a speed of 4 m/s immediately after being kicked by a force of strength 20N... 16. A wooden block of mass M is moving at speed V in a straight l

### Impulse with Constant Velocity

An 79.1 kg astronaut is working on the engines of his ship, which is drifting through space with a constant velocity. The astronaut, wishing to get a better view of the Universe, pushes against the ship and much later finds himself 30.4 m behind the ship. Without a thruster, the only way to return to the ship is to throw his 0.5

### Mechanics and Projectile Motion

Please help with these two mechanics questions: 1. A punter kicks a football at an angle of 33.1 degrees with the horizontal at an initial speed of 24.5 m/s. What distance (in meters) away should a punt returner position himself to catch the ball just before it strikes the ground? And to what vertical height (in meters) does t

### Period of a pendulum - amplitude

When the amplitude of a pendulum decreases to half its initial value. Will the period have doubled, halved or stayed the same?