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Classical Mechanics

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

Skydivers free fall traveling speeds

A skydiver in free fall travels at a speed modeled by V(t) = 176(1 ?e^?0.18 t) ft per second after t seconds. How long will it take for the skydiver to attain the speed of 60 mph (note: 60 mph = 88 ft/sec)? (See attached file)

Minimum Coefficient of Static Friction

For the situation shown in the figure, what is the minimum coefficient of static friction between the block and the surface that will keep the block from moving? (F1 = 5.0 N, F2 = 4.0 N, and m = 5.0 kg.) See Attached

Classical Mechanics: Crate and Friction

A student could either pull or push, at an angle of 300 from the horizontal, a 50-kg crate on a horizontal surface, where the coefficient of kinetic friction between the crate and surface is 0.20. The crate is to be moved a horizontal distance of 15 m. (a) Compared with pushing, pulling requires the student to do (1) less,

Physics - Classical Mechanics - Inclined Plane

A packing crate is placed on a plane inclined at an angle of 350 from horizontal. If the coefficient of static friction between the crate and the plane is 0.65, will the crate slide down the plane? Justify your answer.

Residence Time of Water

A stable and highly soluble pollutant is dumped into a lake at the rate of 0.19 tonnes per day. The lake volume is 2E7 m3 and the average water flow-through rate is 8E4 m3 per day. Ignore evaporation from the lake surface and assume the pollutant is uniformly mixed in the lake. What eventual steady-state concentration will t