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Classical Mechanics

Pascal's Principle

The digging bucket on a large mechanical excavator is moved by a piston sliding within a single hydraulic cylinder. According to the manufacturer, the hydraulic fluid in the cylinder is pressurized to 1000 psi (6.895 x 10^6 Pa or 68 atm) by a pump. The cylinder has a diameter of 0.165 m and a stroke of 1.36 m. Determine the ma

Critical stress, stress field

Question 3 Tensile tests of an elastic material show that it has a Young's modulus of... Please see attached past exam questions

Poisson Ratio, Young's modulus

Please see attached past exam questions: (a) A material has a shear modulus of 4.615.... (b) Hence show that Young's modulus is...

Mechanics and Young's Modulus

For the cross-section of the following figure, which is made from material with Young's modulus 100MN/m^2: (a) State the location of the centroid. (b) Show that the second moments of area about the z axis and teh axis aa are respectively 2.51x10^5 mm^4 and 1.26x10^6 mm^4. (c) A strut is made of this section. When subject to

CT scanner

A CT scanner has to be able to form an image within a 40cm diameter image area. The spatial sampling along each profile is 1mm. What angular resolution (the angle between projections) is required to match this sampling distance at the boundary of the image area?

Tension on a bridge cable

A knight in armour on a horse leaves the castle. His squire has mistakenly lowered the drawbridge 20 degrees below the horizontal. The knight and his horse stop when their combined center of mass are 1 metre from the end of the bridge. The uniform bridge is 8 metres long and has a mass of 2000 kg. The lift cable is attached t

Hitting a Tennis Ball

The tennis ball has a horizontal speed of 15 m/s when struck by the racket. If it then travels away at an angle of 25 degrees from the horizontal and reaches a maximum altitude of 10m, measured from the height of the racket, determine the magnitude of the net impulse of the racket on the ball. The ball has a mass of 180g. Neglec

Loaded Sullivan's Perfect Ratchet

Show that in the case of zero external force the equation v=(fL/kT)^2 D/L (e^(fL/kT) - 1 - fL/kT)^-1 reduces to 2D/L. Then show that at high force (but still smaller than (epsilon/L)) the equation reduces to v=(fL/kT)^2 D/L (e^(-fL/kT)).

Sliding Box

The 30-lb box A is released from rest and slides down along the smooth ramp and onto the surface of a cart. If the cart is fixed from moving, determine the distance s from the end of the cart to where the box stops. The coefficient of kinetic friction between the cart and the box is uk= 0.6.

Volume and density problem

A block of wood half as dense as water floats with half its volume above water. A piece of iron is then tied on top so the wood floats with only 1/4 its volume above surface. If the wood and iron are turned over so that the iron is submerged beneath the wood, then the volume of wood above the water surface will be? Why?

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

Projectile motion

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

Uniform cylinder, moment of inertia by translation of axis.

A uniform cylinder, has mass 18 kg and radius .5 m. Its moment of inertia about an axis which is .3 m from the center of mass axis, is 3.87 kg m^2. Each axis is perpendicular to the circular face of the cylinder. Find the moment of inertia about an axis at the surface of the cylinder.

Kinematics problem

A car travels 600. m one way with a speed of 40. m/s and then travels 600. m in another way at 20. m/s.What is the car's average speed? (Caution: The answer is not 30. m/s.)

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

Derive an expression for F such that θ does not change with time and block

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 θ (block #2 is hanging there, not touching block #3). An external force F i

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