A small block with mass 0.0400 kg is moving in the xy-plane. The net force on the block is described by the potential- energy function U(x,y)= (6.00 J/m2 )x2-(3.40 J/m3 )

Part A

What is the magnitude of the acceleration of the block when it is at the point x= 0.31 m , y= 0.61 m ?

Part B

What is the direction of the acceleration of the block when it is at the point x= 0.31 m , y= 0.61 m ?

Two particles each with charge +2.14

A 12.0m uniform beam is hinged to a vertical wall and held horizontally by a 5.00m cable attached to the wall 4.00m above the hinge, as shown in the figure below (Figure 1) . The metal of this cable has a test strength of 1.00kN , which means that it will break if the tension in it exceeds that amount.

What is the heaviest beam that the cable can support with the given configuration?

Find the horizontal component of the force the hinge exerts on the beam.

Find the vertical component of the force the hinge exerts on the beam.

A positive charge of magnitude Q₁ = 9 nC is located at the origin. A negative charge Q₂ = -9 nC is located on the positive x-axis at x = 18.5 cm from the origin. The point P is located y = 8.5 cm above charge Q₂.

Calculate the x-component of the electric field at point P due to charge Q₁. Write your answer in units of N/C.

Calculate the y-component of the electric field at point P due to charge Q₁. Write your answer in units of N/C.

Calculate the y-component of the electric field at point P due to the Charge Q₂. Write your answer in units of N/C.

Calculate the y-component of the electric field at point P due to both charges. Write your answer in units of N/C.

Calculate the magnitude of the electric field at point P due to both charges. Write your answer in units of N/C.

Calculate the angle in degrees of the electric field at point P relative to the positive x-axis.

(1 point) An 4-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 20 N/m and the damping constant is 2 N-sec/m. At time t=0t=0, an external force of F(t)=2cos(2t+π4)F(t)=2cos⁡(2t+π4) is applied to the system. Formulate the initial value problem describing the motion of the mass and determine the amplitude and period of the steady-state solution.

Let y(t)y(t) to denote the displacement, in meters, of the mass from its equilibrium position. Set up a differential equation that describes this system. (give your answer in terms of y,y′,y′′y,y′,y″).

I will be happy if you show me your best explanation. I will provide a thumb up if you solve correctly.

8. Two identical piano wires have a fundamental frequency of 650 Hz when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 8 beats/s when both wires vibrate simultaneously? Answer: ( which one: 0.0248 or 0.0246 and why)

9. A stone is dropped into a well. The sound of the splash is heard 3.5 s later. What is the depth of the well? Take the speed of sound in air to be 343 m/s. Answer: a=7.4 h=54.8m

Two converging lenses, the first with focal length 10.0 cm and the second with focal length 20.0 cm, are separated by 40.0 cm. An object, 3.00 cm in height, is placed 30.0 cm in front of the first lens. Which of the following characteristics does the final image have? real and upright real and inverted virtual and upright virtual and inverted none of these choices are correct

Suppose a cyclotron is operated at an oscillator frequency of 10.0 MHz and has a dee radius 42.9 cm. Estimate the total path length traveled by a deuteron in the cyclotron during the (entire) acceleration process. Assume that the accelerating potential between the dees is 94.9 kV. The deuteron mass is m = 3.34x10^-27 kg.

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -4q. Sphere B carries a charge of -5q. Sphere C carries no net charge. Spheres A and B are touched together and then separated. Sphere C is then touched to sphere A and separated from it. Last, sphere C is touched to sphere B and separated from it. For the following questions, express your answers in terms of q.

(a) How much charge ends up on sphere C?

(b) What is the total charge on the three spheres before they are allowed to touch each other?

(c) What is the total charge on the three spheres after they have touched?

Please answer all three parts if possible and show all steps. Thanks in advance!

Two 15-cm-diameter metal disks separated by a 0.59-mm-thick piece of Pyrex glass are charged to a potential difference of 1600 V .

A) What is the surface charge density on the disks?

η =   (in μC/m^2)

B) What is the surface charge density on the glass?

η (glass) = (in μC/m^2)

With the water in the tube at the level for the tube length L1 of the first resoance of the first tuning fork,

(a) would another tuning fork with a frequeny lower than that of the first tuning fork produce a resonance?

(b) would another tuning fork of some higher frequency produce a resonance?

(c) if your answer is es in either case, what would be the frequency of the other fork?

8. A ball with radius 10 cm is held completely under water (density 1000 kg/m^3).

  a) What is the buoyant force acting on the ball?

  b) If the ball has a mass of 100 g, how much force is required to hold it in place under water? In which direction must this force be applied?

So, I was reading my textbook in the section regarding net torque, and they gave an example of a seesaw with one person at each end, and they said that there is a net external torque due to the force of gravity on each person. I completely understand that; however, when I was reading another section of my textbook, they were talking about the conservation of angular momentum, which only happens when the net torque is zero. So they gave an example of a circular disk that rotates freely in a horizontal plane about a frictionless, verticle axle. On top of that, there is a person who walks slowly from the rim of the disk towards the center. The textbook modeled this problem as conservation of angular momentum problem, but why? Isn't the weight of the person causing an external torque just how the weight of the two people in the seesaw caused a net external torque?

A 1.70-m-long barbell has a 25.0 kg weight on its left end and a 37.0 kg weight on its right end.If you ignore the weight of the bar itself, how far from the left end of the barbell is the center of gravity? Where is the center of gravity if the 9.00 kg mass of the barbell itself is taken into account?

A 230 g , 24-cm-diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 2000 rpm in 5.0 s ?