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    Classical Mechanics

    cSteel Piano string

    The lowest note on a grand piano has a frequency of 27.5 Hz. The string is 2 m (more or less; let's just assume it is exactly 2.000 m) long, and its tension is 1000 N (again, more or less, so let's say it's exactly 1000 N). 1. What must the length density ? (mass per unit length, in units of kg/m or g/m) of the string be

    Wavelengths on a String

    Problem 21.10 Part A What are the three longest wavelengths for standing waves on a 171- -long string that is fixed at both ends? Enter your answers in descending order separated by commas. ANSWER: , , = Answer not displayed Part B If the frequency of the second-longest wavelength is 59 , what is the fr

    Physics: Compression of column; constant of a spring

    1. A 4.8-m-tall, 30-cm-diameter concrete column supports a 5.0Ã?105 kg load. By how much is the column compressed? 2. One end of a spring is attached to a wall. A 30 N pull on the other end causes the spring to stretch by 3.0 cm. What is the spring constant?

    Universal Beam Section: Bending, Maximum Stress

    A universal beam section has a second moment of area about its neutral axis of 6487 cm4 and its overall depth is 305 mm. The beam is simply supported at each end over a length of 5 m and carries a uniformly distributed load of 10 kN m-1 (including its own weight) over its whole length. Modulus of elasticity (E) = 210 GN m-2.

    Speed of car at bottom of driveway; initial speed bullet

    20 A 2.10 x 10³ kg car starts from rest at the top of a 5.0 m long driveway that is sloped at 20° with the horizontal. If an average friction force of 4.0 x 10³ N impedes the motion, find the speed of the car at the bottom of the driveway. 21. An 8.00 g bullet is fired into a 2.5 kg block that is initially at rest at the e

    Collision of 2 trains and stopping distances

    Two trains are driving towards each other .One at 144 km/h and the other at 72 km/h When they see each other they start to brake at 1 m/s2. There is 950m between them. Will they hit each other or will they stop in time?

    Three sleds being pulled horizontally, find the tension in rope

    See attached figure for this problem. Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (the figure ). The pull is horizontal and of magnitude 125 N. Acceleration was found to be 2.08 m/s^2. a) Find the tension in rope A. b) Find the tension in rope B.

    Two curling stones - calculate speed, resistive force

    Two curling stones A and B, each having a mass of 2 kg, are on an ice rink floor. A is stationary and 10 meters from a boundary wall, while B is sliding at right angles to the boundary wall towards A. Stone B collides with A head-on with a speed of 8.1m/s. After the collision stone A moves towards the wall perpendicular t

    At what speed would your 4.98 m long car fit

    Part 1 When parked, your car is 4.98 m long. Unfortunately, your garage is only 4.19 m long. How fast would your car have to be moving (in c) for an observer on the ground to find your car shorter than your garage? Do not enter unit. Part 2 When you are driving at this speed, how long is your garage, as measured in the

    Calculate the focal length required of glasses to be worn

    A pair of eyeglasses are designed to allow a person with a near-point distance of 2.52 m to read a road sign at a distance of 25.2 m. Calculate the focal length required of these glasses if they are to be worn 2.18 cm from the eyes. Please solve and explain.

    Shear stress and vertical deflection

    A horizontal aluminum rod 4.2 cm in diameter projects 7.6 cm from a wall. A 1400 kg object is suspended from the end of the rod. The shear modulus of aluminum is 3.0·1010 N/m2. Neglecting the rod's mass, find (a) the shear stress on the rod and (b) the vertical deflection of the end of the rod (in cm).

    Child's weight, magnitude of force, maximum angle

    A makeshift swing is constructed by making a loop in one end of a rope and tying the other end to a tree limb. A child is sitting in the loop with the rope hanging vertically when the child's father pulls on the child with a horizontal force and displaces the child to one side. Just before the child is released from rest, the ro

    Time required to row cross the river

    A river man can row his boat at a speed of 2.5 m/s through still water. He wants to row directly across a river that has a current flowing at 1.5m/s. Starting from one bank, he rows his boat directly across the river (boat always pointed perpendicular to opposite bank) but reaches a point 50m downstream due to being swept by the

    Physics: Solve a population doubling question

    An easy way to find the time it takes for compound interest to double an investment is to divide 72 by the interest rate in percent. For example, money invested at 3% interest will double in 72/3 = 24 years. This can also be used to compute population doubling. If the current population growth rate is about 2%, when will the wor

    Shear force and bending moment diagrams, maximum bending stress

    See attached files. prob6.JPG Indicate negative and positive regions. Show values of shear and bending moments at points of interests (A,B,C,D,E). prob7.jpg Use loading from previous problem (prob6.jpg). Determine the maximum bending stress that occurs, assume loading is done halfway through the width.

    Find magnitude of tension in a cable

    See attached file. Find (a) the magnitude of the required tension in cable AC, knowing that the resultant of the three forces (F1,F2,T) exerted at point C of boom BC must be directed along BC, (b) the corresponding magnitude of the resultant.

    Physics: Standing Waves, Second Harmonic

    Two pieces of steel wire with identical cross-sections have lengths of L and 2L. Each of the wires is fixed at both ends and stretched so that the tension in the longer wire is three times greater than that in the shorter wire. If the fundamental frequency in the shorter wire is 64.1 Hz, what is the frequency of the second harmo

    Initial kinetic energy of an object

    Point A is situated at the bottom of a rough plane which is inclined at 45 degrees to the horizontal. A body of mass 0.5 kg is projected from A along and up the line of greatest slope. The coefficient of friction between the body and the plane is 3/7. The body first comes to rest at a point B, at a distance 4*2^(1/2) from A, b

    Projectile Motion: Maximum Height and Range

    An arrow is shot at 30.0° above the horizontal. Its initial speed is 45 m/s and it hits the target. (a) What is the maximum height the arrow will attain? ___ m (b) The target is at the height from which the arrow was shot. How far away is it? ___ m

    Determining Tension in a Cable

    See picture attached. Joe wishes to hang a sign weighing 785 N so that cable A attached to the store makes a 30.0° angle, as shown in Figure 7-16. Cable B is horizontal and attached to an adjoining building. What is the tension in cable B? ________N

    Pulling a car from a ditch

    To pull a car from a ditch, the driver ties one end of a rope to the car and the other to a tree 12.5 m away. Driver then pulls sideways from the midpoint of the rope with a 475 N force. How much force exterted on the car when the rope has been pulled 75 cm to one side?

    Classical Mechanics: Projectile Motion

    A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.80 m/s at an angle of 21.0° below the horizontal. It strikes the ground 3.00 s later. (a) How far horizontally from the base of the building does the ball strike the ground? (b) Find the height from which the ball was thr

    Hydraulic machine

    In the hydraulic system shown in Figure 15-28 the piston on the left has a diameter of 4.9 cm and a mass of 1.7 kg. The piston on the right has a diameter of 12 cm and a mass of 2.9 kg. If the density of the fluid is 750 kg/m3, what is the height difference h between the two pistons? ____ m Figure 15-28 SEE ATTACHMENT

    Transvers waves: Speed of wave on stretched string.

    Two steel wires are stretched with the same tension. The first wire has a diameter of 0.610 mm and the second wire has a diameter of 0.910 mm. If the speed of waves traveling along the first wire is 54.0 m/s, what is the speed of waves traveling along the second wire?

    Speed and direction

    Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 4.0 mi/h, the time to go one mile decreases by 12 s. What was your original speed? ....... mi/h ?

    Bernoulli's Equation for a Rectangular Roof

    The construction of a flat rectangular roof (3.9 m x 4.3 m) allows it to withstand a maximum net outward force of 20050 N. The density of the air is 1.27 kg/m3. At what wind speed will this roof blow outward?

    Tension and Weight in Water

    Part A: A raft floats and displaces 4.5 m^3 of water. The volume of the raft id 8 m^3 and its area is 10 m^2. When the tide is low the raft is attached to an anchor. As the tide comes in the water level rises .25 m but the raft is constrained and rise. What is the tension on the anchor? Part B: If the raft is taken to the Dea