. You have constructed a pendulum by tying a 760 g mug to a 73 cm string. You pull the mug 21 degrees to the side, then you release it. a) Draw an illustration of the pendulum, labeling all information known. b) What are the kinetic and potential energy at the top and bottom of the swing? c) What is the work done by gravity from top to bottom of the swing? d) What is the work done by the string from the top to the bottom of the swing? e) Assuming negligible air resistance, what is the mug’s speed when its at the lowest point in its swing? f) Draw the free-body diagram for the mug when the string is 10 degrees from vertical. g) What is the mug’s radial and tangential acceleration when the string is 10 degrees from vertical? h) What is the tension in the string when the mug is at the bottom of its swing? i) At what angle is the tension in the string equal to the weight of the mug?

Please show all work and formulas!

4. A strong microscope objective lens "100

please answer all questions

1.) Which of the types of energies in the electromagnetic spectrum have the ability to ionize?

2.) What makes an x-ray photon higher energy than a microwave?

3.) State the wave equation

A 1700kg car starts from rest and drives around a flat 68-m-diameter circular track. The forward force provided by the car's drive wheels is a constant1300N .

What is the magnitude of the car's acceleration at t=12s?

What is the direction of the car's acceleration at t=12s? Give the direction as an angle from the r-axis.

If the car has rubber tires and the track is concrete, at what time does the car begin to slide out of the circle?

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?