A chain fixed at its ends and subject to uniform gravitational force hangs in the shape of a catenary curve. A parameterization for this curve is r(t)= <t, a cosh t/a +b> Where a and b are constants. You have a 12 ft chain and hang it with its ends on hooks at (-5,10) and (5,10). Find the values for a and b that describe the resulting curve. What is the height of the lowest point of the chain?

Show that the total energy of a harmonic oscillator in the absence of friction is conserved.

An elevator system in a tall building consists of a 800-kg car and a 950-kg counterweight joined by a light cable of constant length that passes over a pulley of mass 280 kg. The pulley, called a sheave, is a solid cylinder of radius 0.700 m turning on a horizontal axle. The cable does not slip on the sheave. A number n of people, each of mass 80.0 kg, are riding in the elevator car, moving upward at 3.00 m/s and approaching the floor where the car should stop. As an energy-conservation measure, a computer disconnects the elevator motor at just the right moment so that the sheave–car– counterweight system then coasts freely without friction and comes to rest at the floor desired. There it is caught by a simple latch rather than by a massive brake. (a) Determine the distance d the car coasts upward as a function of n. Evaluate the distance for (b) n = 2, (c) n = 12, and (d) n = 0. (e) For what integer values of n does the expression in part (a) apply? (f) Explain your answer to part (e). (g) If an infinite number of people could fit on the elevator, what is the value of d ?

Design a synchronous counter, using T flip-flops, that has the following sequence: 0010, 0110, 1000, 1001, 1100, 1101, and repeat. From the undesired states the counter must always go to 0010 on the next clock pulse.

The force acts on a particle
F = 2xy ^ 2i + 2x ^ 2yj N
Find the work done by force by moving the body from the point (0,0) to the point (2,4) following the following paths

1) (0,0) -----> (2,0) -----> (2,4)

2) (0,0) ----> (0,4) ----> (2,4)

3) Along the line that joins both points

4) Along the parabola y = x ^ 2

5) Is a conservative force?

Please make the graphs and justify all your answers please like why the force is o nor conservative

A block of pine wood (p=.43 g/cm³) is floating on a pond. The block is 10 cm x 40 cm x 5 cm thick.

a) How much of the block protrudes above the water?

b) If the block is made to carry a load by placing additional mass on top of it, how much mass must be added to just submerge the block?

Please show all work. Thank you for the help!!!

Describe the photo electric event experimentally. Why can't the photoelectric phenomenon be explained by classical physics?

Please can someone double-check my answers?

1) A ball with a mass of 0.15 kg has a velocity of 5m/s. It strikes a wall perpendicularly and bounces off straight back with a velocity of 3 m/s. The ball underwent a change in momentum of?

1.20 kg*m/s

2) What braking force is supplied to a 3,000 kg car traveling with a velocity of 35 m/s that is stopped in 12 seconds?

F=8750 N

3) A 0.1 kg baseball is thrown with a velocity of 35 m/s. The batter hits it straight back with a velocity of 60 m/s. What is the magnitude of the average impulse exerted on the ball by the bat?

9.5 N*s

4) A 1 kg object is moving with a velocity of 6 m/s to the right. It collides and sticks to a 2 kg object moving with velocity of 3 m/s in the same direction. How much Kinetic energy is lost in the collision?

3J

5) A 2 kg mass moving with a velocity of 7 m/s collides elastically with a 4 kg mass moving in the opposite direction at 4 m/s. The 2 kg mass reverses direction after the collision and has new velocity of 3 m/s. What is the velocity of the 4 kg mass?

1 m/s

6) A mass of 3 kg is attached to a massless spring with a force constant 500 N/m. The mass rests on a horizontal frictionless surface. The system is compressed a distance of 30 cm from the springs initial position and then released. The momentum of the mass when the spring passes its equilibrium position is?

8660.25m/s

7) Can an object have energy without having momentum? Explain.

Yes an object can have energy without having momentum. For example, a rock that is at the top of a cliff has potential energy since it's not moving but there is no momentum.

8) Can an object have momentum without having energy? Explain.

No object that has momentum also has energy. This is because if the velocity is not then the kinetic energy is also not 0 momentum is a vector, but energy is a scalar.

9) An object of mass 2 kg has a linear momentum of 6 kg. m /s. What is this objects Kinetic energy?

9J

10) A box with a mass of 2 kg accelerates in a straight line from 4 m/s to 8 m/s due to the application of a force whose duration is 0.5 seconds. Find the average strength of this force?

16N

11) A 45 kg. girl is sitting on a seesaw 0.6 m from the balance point. How far, on the other side, should a 60 kg. boy sit so that the seesaw will remain in balance?

0.45m

12) A solid cylinder consisting of an outer radius R1 and an inner radius R2 is pivoted on a frictionless axle as shown. A string is wound around the outer radius and is pulled to the right with a force F1 = 3N. A second string is wound around the inner radius and is pulled down with a force F2 = 5N. If R1 = 0.75 m and R2 = 0.35m, what is the net torque acting on the cylinder?

-0.5Nm

15) An object of mass 0.5 kg., moving in a circular path of radius 0.25 m, experiences a centripetal acceleration of constant magnitude 9 m/s2 . What is the objects angular speed?

6 rad/sec

16) An object, originally at rest begins spinning under uniform angular acceleration. In 10 seconds, it completes an angular displacement of 60 rad. What is the value of its angular acceleration?

1.2 rad/s^2

17) The moment of Inertia of a solid uniform sphere of mass m and radius R is given by the equation I = (2/5) mR2 . Such a sphere is released from rest at the top of an inclined plane of height h= 10 m, length L, and the incline angle Ω. If the sphere rolls without slipping, find the linear speed at the bottom of the incline.

11.83m/s

18) An object spins with angular velocity 10 rad/s. If the objects moment of Inertia increases by a factor of 2 without the application of an external torque, what will be the object’s new angular velocity?

1/2 angular velocity (w)

19) A 0.05 kg ball is thrown upward from the ground with an initial velocity of 30 m/s. At its maximum height, the magnitude of the balls acceleration is?

9.80 m/s^2

20) A 15 Newton force is applied to a mass M that is adjacent to a wall, as shown. If the mass is 2 kg, the force that the wall exerts on the mass is equal to?

15N

Demonstrate that the WKB approximation yields the energy levels of the linear harmonic oscillator and compute the WKB approximation for the energy eigenfunctions for the n=0 and n=1 state and compute with the exact stationary state solutions.

Two charges Q1(+2.00µC) and Q2(+2.00µC) are placed symmetrically along the x-axis at x = ±3.00cm. Consider a charge Q3 of charge +5.00µC and

mass 10.0 g moving along the y-axis. If Q3 starts from rest at y=2.00cm, what is its speed when it reaches y=4.00cm?

When a direct current flows through a straight length of wire, what is the direction of the magnetic field that is produced near the wire?
A) The magnetic field is antiparallel to the direction of the current.
B)The magnetic field is perpendicular to the direction of the current.    
C)The magnetic field is parallel to the direction of the current.
D)There is no magnetic field near a wire carrying direct current; direct currents do not create magnetic fields.

You and a friend drag a 28.8 kg fallen tree branch across a level field. You pull with a force of 135.0 N at an angle of 25.0º above the horizontal while a friend’s pull force is parallel to the ground, the kinetic coefficient of friction between the branch and the ground is µk=0.825 and the static coefficient of friction is µs=0.925. The branch starts from rest and is dragged 20.0 m in 15.0 s.

1. What is the acceleration of the branch?
2. What is the magnitude of the normal force acting on the branch?
3. What is the magnitude of your friend’s pull force?
4. If you and your friend were to stop pulling and then your friend leaves, would you be abele to get the branch moving again with the same force? If yes, prove it, if not, what force is needed to start the branch moving?

A ball is thrown straight up with an initial speed of 19 m/s. The ball was released 6.3 m above the ground, but when it returns back down, it falls into a hole d m deep. If the ball’s speed is 35.7 m/s at the bottom of the hole, how deep is the hole (in m)?

A "Linde-machine" is used to cool and liquefy air. The cyclic process uses three different states running
through three different processes, assuming air as a diatomic ideal gas:
1 > 2: adiabatic compression with T1 = 23.0 °C, T2 = 150 °C, p1 = 2.00 x 10^5 Pa and V1 = 2.50 dm^3
2 > 3: isobaric compression with T3 = T1
3 > 1: isothermal expansion
a) Draw the corresponding p(V) diagram of the cyclic process, numbering the different states and indicating
the direction of the individual processes (note that it is not a heat engine, but used to cool air).
b) What are the number of moles, the pressure at state 2 and volumes at states 2 and 3?
c) What are the related work and heat taken up or released at each process?
d) Calculate the total amount of work.