Consider two massless springs connected in series. Spring 1 has a spring constant k_1, and spring 2 has a spring constant k_2. A constant force of magnitude F is being applied to the right. When the two springs are connected in this way, they form a system equivalent to a single spring of spring constant k. a) Find the sprin
8.6. a. A particle has s=3/2. The operator S++ is defined to be the square of the raising operator: S++ = (S+)^2, where S+ is the usual raising operator: S+|sms = h (s(s+1) - ms(ms+1)|sms +1)^1/2 Derive the matrix corresponding to the operator S++. b. What is the matrix corresponding to the adjoint operator (S++)? See
The rigid bar ABCD is suspended from three identical wires as shown. The cross-sectional are of each wire is A, the unloaded length of each wire is L, and the elastic modulus is E. Knowing that a = b, determine the deflection in wire A, B and D caused by the load P applied at C.
A 55.0-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.300. A force of 156 N is applied to the box directed at an angle of 18.0 above the horizontal. Does the box move?
7. A horizontal beam length= 10m, mass= 25kg that is pivoted at the wall, with its far end supported by a cable that makes an angle 50° with the horizontal. If a person with a mass of 60kg stands 3.0m from the pivot, what is the tension in the cable? I need to know all of the forces acting on the beam. 8. A disk of mass M and
The figure below shows a spring/dashpot/mass system, with an extra applied force, F. In terms of K, B, m, and F, what is the differential equation describing the deflection of the mass? What is the Laplace transfer function between input F and output x? See attached file for full problem description.
Using the Euler and Taylor formulas, prove and solve the attached questions. See attached file for full problem description.
(See attached file for full problem description) 11. Consider two objects whose position vectors are given by r1 and r2 and whose momenta are given by p1 = m1v1 and p2 = m2v2 respectively. Show that in the special case that the center of mass of the two bodies is at rest at the origin (that is P = p1 + p2 = 0, and the positi
(See attached file for full problem description) 1. A constant-volume gas thermometer is calibrated in dry ice (-80.0°C ) and in boiling ethyl alcohol (78.0°C ). The respective pressures are 0.900 atm and 1.635 atm. (Note that we have the linear relationship P = A + BT, where A and B are constants.) (a) What value of ab
A gardener pushes a box of tools across a driveway by applying a 32.5 Newton force that pushes downward at an angle of 22.4 degrees with respect to the horizontal. How much work is done if the box moves 2.25 meters in the horizontal direction? I need to see each step and formula to solve this question.
Stretch receptors in lungs are modeled as second-order systems whose input is the applied stretch, x(t), and output is the instantaneous firing frequency of the receptor, y(t). Assume that one such receptor can be described by the differential equation: d^2y/dt^2 + 2*d/dt + 4y(t) = 10x(t) +dx/dt Determine the frequency r
A water wave is called a deep-water wave if the water's depth is more than 1/4 of the wavelength. The speed of a deep water wave depends on its wavelength: v = sqrt((g.lambda)/2pi). Longer wavelengths travel faster. Let's apply to this to a standing wave. Consider a diving pool that is 5.0 m deep and 10.0 m wide. Standing w
Force of a Baseball Swing. A baseball has mass 0.145 kg. 1. If the velocity of a pitched ball has a magnitude of 45.0 m/s and the batted ball's velocity is 55.0 m/s in the opposite direction, find the magnitude of the change in momentum of the ball. 2. Find the magnitude of the impulse applied to it by the bat. 3. If t
18. the leg and cast in picture (attached) weigh 220N (w1) Determine the weight w2 and the angle needed so that no force is exerted on the hip joint by the leg plus the cast. 41. The coefficient of static friction between a 3.00 kg crate and the 35.0 degree incline it sits on is 0.300. What minimum force (F) must be appl
Find the equation of motion for the Atwood machine depicted in the diagram.
A steel wire of length 2.06 m with circular cross section must stretch no more than 0.290 cm when a tensile force of 350 N is applied to each end of the wire. 1. What minimum diameter d_min is required for the wire? Express your answer in millimeters. Take Young's modulus for steel to be Y = 2Ã ?1011 Pa.
What force must be applied to a small cylinder piston with a diameter of 0.32 m to lift a car weighing 12,000N that is supported by the piston in a large cylinder that has a diameter of 1.4m? Assume that there is a closed chamber in the common between the two pistons and that the chamber is filled with hydraulic oil.
A horizontal 808 N merry-go-round is a solid disk of radius 1.56 m, started from rest by a constant horizontal force of 50.5 N applied tangentially to the edge of the disk. Find the kinetic energy of the disk after 2.96 s.
Balls A and B roll across a table, then collide elastically. The paths of the two balls are pictured (viewed from above) in the diagram. (See attachment for diagram)
A force is applied to the end of a 2.0ft long, uniform board weighing 50lbs. in order to keep it horizontal and stationary while it pushes against the wall at the left. if the angle the force makes is 30 degrees towards the left, what is the magnitude of the applied force F?
The blue box in the figure has a mass of 38 kg. To the nearest newton, what is the tension in the rope? If the spring has a spring constant of 515 N/m, to the nearest tenth of a cm how far is it stretched? See the attached file.
A 110-kg box is loaded into the trunk of a car. If the height of the car's bumper decreases by 13 cm, what is the force constant of its rear suspension?
An object in motion stays in motion until it comes into contact with a opposite greater or equal force.
A force of 1.0 * 10^3 N is applied to a steel rod of length 1 m and a circular cross-section of area 10 cm^2. Find the elongation of the rod. Young's modulus for steel is 2.0 * 10^11 Pa.
Please see attached for question.
Imagine a hydraulically operated dentist's chair having a mass of 200.0 kg, and in it is sitting a 54.8-kg patient. The large piston beneath the chair has a diameter of 5.00 cm, whereas the small piston, moved by a pedal on which the dentist steps, has a diameter of 1.00 cm. What is the pressure in the interconnecting fluid wh
Two identical books each with k pages are placed on the table in a way that the each page of book A is between the pages of book b. The high half of book B is on top of book A. Given that 1) the coefficient of static friction on the surface of card A is mu; 2) Each page of the book has a mass of m; 3) Book A does not move f
A person holds a bowling ball in his hand with his forearm horizontal. The bowling ball has a mass of 5.10 kg and the mass of the forearm is 1.50 kg. The bicep muscle is attached to the bone of the forearm at a point d=3.00 cm from the elbow joint and the bowling ball is L=35.0 cm from the joint. Model the center of mass of the
Find Fmin, the constant force with the least magnitude, that must be applied to the board in order to pull the board out from under the box (which will then fall off of the opposite end of the board).
Prove that when two springs are attached one at the end of the other, the coefficient of the final spring becomes 1 / (1/k1 + 1/k2 ) where k1 and k2 are the coefficient of the two individual springs, the direction of the springs is VERTICAL not horizontal. Then consider two systems of springs, one in which a mass m is attached t