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# Classical Mechanics

### Classical mechanics problems - vectors operations and uniform acceleration

13. A bus travels at an average speed of 90 km/h. On average, how far does the bus travel in 20 min? Is this distance the magnitude of the actual displacement of the bus? Explain. 17. A student runs 30 m east, 40 m north, and 50 m west. (a) The magnitude of the student's net displacement is (1) between 0 and 20 m, (2) bet

### Misc problems dealing with units conversions, volume, density velocity and distance.

A corner construction lot has the shape of a right triangle. If the two sides perpendicular to each other are 37 m long and 42.3 m long, respectively, what is the length of the hypotenuse? 75. The lightest solid material is silica aerogel, which has a typical density of only about 3 0.10 g/cm . The mole

### Direction of Movement of a Balloon in an Accelerating Car

A helium-filled balloon is being transported in a car. As the car accelerates away from a stop light, in which direction does the balloon move relative to the car? Thank you!

### Projectile motion

A missile is launched at a speed of 25 m/s at an angle of to 35&#61616;&#61472;the ground. What is its range? How high did it go vertically? Answer without using calculus.

### What is the coefficient of kinetic friction between the pig and the slide?

A slide-loving pig slides down a 37° incline (Fig. 6-24) in twice the time it would take to slide down a frictionless 37° incline. What is the coefficient of kinetic friction between the pig and the slide?

### Finding the Center of Mass of a Nonlinear Thin Rod

A thin non-uniform rod is 4 meters in length and has a linear density D, (mass per unit length), in kg/m, which is expressed by D= 3 + 5 x in which x is the distance in meters from the zero end of the rod. Find the x coordinate of the center of mass of the rod.

### Elasticity: Tensile stress - normal, tangential; shear stress

See attached diagram. A bar with cross sectional area A is subjected to equal and opposite tensile forces F at its ends. Consider a plan through the bar making an angle ? with a plane at right angles to the bar. a.) What is the tensile (normal) stress at this plane in terms of F, A, and ? ? b.) What is the shear (tange

### What is the largest mass Tarzan can have and swing safely across the river?

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.0 m long. His speed at the bottom of the swing, just as he clears the surface of the river, is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 x 10^3 N. What is the largest mass Tarzan can have and make it safe

### Physics momentum and center of mass: How far will the boat move?

Two people, one of mass 75.6 kg and the other of mass 60.2 kg, sit in a rowboat of mass 82.4 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 2.02 m apart from each other, now exchange seats. How far will the boat move?

### Pressure in Pascals for high heel shoe print

A high heel shoe leaves a foot print on the floor. The front area part of the print has an area or 32.5 cm squared. The heel of shoe leaves a 1 cm circle imprint. Standing on one leg, what pressure in pascals would you exert on the floor, assuming you weigh 165 lbs? How deep would one need to dive in fresh water in order to

### Deriving Expression for Block Configuration

See attached file. Three blocks are configured as in the attachment. A string is attached from block #1 to block #2 (looped over a pulley), and the angle between the string going from mass #2 to the pulley, with respect to straight downward, is &#952; (block #2 is hanging there, not touching block #3). An external force F i

### Strategy to find speed of hockey puck at launch and as it leaves the rink

A hockey puck just clears the 2.00-m high boards on its way out of the rink. The base of the boards is 20.2 m from the point where the puck is launched. a. given the launch angle of the puck (-), outline a strategy that you can use to find its initial speed Vo. b. use your strategy to find Vo for (-) = 15.0 degrees.

### Find the magnitude of two identical positive charges

Two identical positive charges separated by a distance of 1X10^-5m have a potential energy of 1X10^-10 Joules. Find the magnitudes of these charges.

### Find maximum force P on Block A such that B does not slide relative to Block A.

SEE ATTACHMENT #1 for a diagram with parameters. Block B whose weight B= 22 nt, is placed on top of Block A whose weight is A= 44 nt. The coefficient of friction for all surfaces is f= .20. A horizontal force P is applied to A to slide both objects across the horizontal table. Find the maximum force P such that block B d

### Physics of Matter: Weight of aluminum part in an aircraft engine

A certain part of an aircraft engine has a volume of 1.3 ft cubed. Find the weight of the piece when it is made of aluminum.

### Find height of building after a rock and a marble are thrown downward.

From a rooftop, a rock is released at rest and 2 seconds later, a marble is thrown downward from the roof with initial speed of 24.5 m/sec. Both hit the ground at the same instant. Find the height of the building.

### Find the cable tension.

An apparatus consisting of a wood block of density 650 kg/m^3 and mass M= 64 kg, is attached by a cable to a cement block of density 4500 kg/m^3 and mass 125 kg. The cement block rests on the sea bottom, and holds the wood block stationary above it. The sea density is 1025 kg/m^3. Find the tension in the cable.

### Two ships receive signals from the bottom at different times. Find the depth of the sea.

SEE ATTACHMENT #1 for a diagram of the situation. Two research ships are distance S= 3600 meters apart on the ocean surface. Ship A now drops an explosive device overboard which sinks and explodes upon reaching the bottom. The sound of the explosion is received by A, directly above, 1.5 seconds before it is received by B. A

### A page of extremely useful formulas for mechanics.

Equations include those for linear motion, rotary motion, momentum, energy, etc. This is a great study tool, if a student is capable of understanding and using these formulas they should be able to do well on any exam in this area.

### Physical pendulums with SHM.

A thin uniform ring, placed on a knife edge pivot executes SHM period 'Tr'. The same ring is cut, then straightened to form a bar, which executes SHM with a period 'Tb'. Find the ratio of periods, Tb/Tr.

### Equation of x(t) for a certain point moving with SHM

The position x of a certain SHM is expressed by: x = (.25 m) cos (8 t). PART a. Take derivatives to write v(t) and a(t). PART b. ATTACHMENT #1 shows general sine or cosine curves with the time axis shown. The location of the vertical axis, not shown, depends on the equation for t=0. For each equation, make a vertical axis

### A multi part calculation about volume flow rates in a leaking tank

A tank of oil, p=670kg/m^3, develops a leak. The leak is 6m below the open surface of the tank. A. If the leak is circular with a 7.5cm diameter, and the tank is 1.0 in diameter, what is the current volume flow rate of oil leaving the tank? Do not assume the tank is large compared to the leak. B. In time the leak will be 5

### A cube suspended in water by a cord; find mass and force

A cube of aluminum, whose volume is Va= .125 m^3, and whose density is Da= 2700 kg/m^3 is suspended from a cord which holds it stationary with the top surface horizontal and h= 2.2 m below the surface of fresh water. See attachment #1 showing known parameters. PART a. Find the mass of the aluminum. PART b. Find C, the force

### Physics: The Speed of a Wave. What is the mass of the string?

A 0.75 m string is stretched so the tension is 2.3N. A transverse wave with a frequency of 150 Hz and a wavelength of 0.40 m travels on the string. What is the mass of the string?

### Physics: Mathmatical description of a wave; time, direction, displacement

The displacement (in meters) of a wave is y= 0.26 sin((pie)t-3.79(pie)x, where t is in seconds and x is in meters. (a) Is the wave traveling in the +x or-x direction? (b) What is the displacement of y when t= 38s and x=13m?

### Proton collision

A proton makes a head-on collison with an unknown particle at rest. The proton rebounds straight back with 4/9 of its initial kinetic energy. Find the ratio of the mass of the unknown particle to the mass of the proton, assuming that the collision is elastic

### Frequency of Vibration Denoted

A particular guitar string is supposed to vibrate at 199.1 Hz, but it is measured to actually vibrate at 214.2 Hz. By what percent should the tension in the string be changed to cause the string to vibrate at the correct fundamental frequency? [Enter the percentage only; do not enter units.]

### Calculating the tension of a string.

A solid object made out of lead has a volume of 24.0 cm3 and is supported (from above) by a string while the object is completely submerged in water. What is the tension in the string?