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Classical Mechanics

Static Friction and Dual Block System

One block rests upon a horizontal surface. A second identical block rests upon the first one. The coefficient of static friction between the blocks is the same as the coefficient of static friction between the lower block and the horizontal surface. A horizontal force is applied to the upper block, and its magnitude is slowly in

Irradiance of a Source

Show that the height of a light bulb (assumed to be a point source) from the center of a circular table radius = a that provides a maximum irradiance at its edges is given by 2(a) ^ (1/2)

Finding the Frequency of Oscillatory Motion

Two masses M=100gms. and Q = 200gms. slide freely on a horizontal, frictionless track and are connected by a spring whose force constant is k = .5 Newtons/meter. Find the frequency of oscillatory motion for this system.

Determining Horizontal Distance

A horizontal rifle is fired at a bull's eye. The muzzle speed of the bullet is 670 m/s. The barrel is pointed directly at the center of the bull's eye, but the bullet strikes the target .025 m below the center. What is the horizontal distance between the end of the rifle and the bull's eye?

ballast bag released from a rising balloon

A balloon is rising straight up with a speed of 3.0 m/s. A ballast bag is released from rest relative to the balloon when it is 9.5 m above the ground. How much time elapses before the ballast bag hits the ground?

Speed question

A diver runs horizontally with a speed of 1.20 m/s off a platform that is 10 m above the water. What is his speed just before striking the water?

Mechanics and Arbitrary Vectors

Show that: a. Sum of vectors i and j: epsilon(ijk)delta(ij) =0 b. Sum of vectors j,k: epsilon(ijk)epsilon(njk) = 2delta (in) c Sum of vectors i,j,k: epsilon(ijk)epsilon(ijk) = 6 Show that: Sum of vectors k: epsilon (jk)epsilon (mnk) = delta(im)delta (jn) - delta (in)delta (jm) Using the epsilon (ijk) notation and in f

Questions involving different gravities and masses

15. The height achieved in a jump is determined by the initial vertical velocity that the jumper is able to achieve. Assuming that this is a fixed number, how high can an athlete jump on Mars if she can clear 1.55 In on Earth? 22. The radius of a neutron star is T50 times smaller than Earth's radius, and its mass is 1.8 H 105

A system of two masses

A cart of weight m1 is pulled uphill on a 15 degrees slope by a bucket of weight m2 dropping vertically. Ignoring friction and the weight of the cable, determine how m1 and m2 must be related in order for the system to move with constant speed.

Radio frequency reception

A shortwave receiver has "90-m band" written on one end of the dial and "11-m band" on the other. What range of frequencies does this radio receive? Take the speed of radio waves to be 3.00 × 10^8 m/s.

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?

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?

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 ρ 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