Newton’s Law of Motion

Part 2 data: Tilted Track

(PLEASE SHOW ALL WORK)

1. Draw four FBD (free body diagrams) with Fnet vectors for the following four cases. (Neglect friction and drag.) (Define coordinate systems for each object, where each coordinate system is aligned with the object’s acceleration.)

a. Hanging mass while accelerating down (b). Cart on flat track while accelerating (from part 1 data)

c. Cart on inclined track while accelerating (d). Cart on declined track while accelerating (this is from part 2 data)

2. For case 1a above, write out Newton’s 2nd Law in the y-direction and solve for the tension: TH.

3. For cases 1b, 1c, and 1d, write out Newton’s 2nd Law in the x-direction and solve for the tension: TC.

4. Start an Excel data table and organize all your data (angles, mC, mH, and cart accelerations)

5. Nearby, start an Excel results table. Here, calculate the following quantities once per trial.

Reminder: If you use sine or cosine in MS Excel, it expects the angle to be entered in radians. You can input degrees by using “sin(radians(A1))” and “cos(radians(A1))”.    (Change “A1” to match your angle’s location.)

a. the net force acting on the cart, using Fnet=ma.

b. the net force acting on the hanging mass, using Fnet=ma.

c. the tension force, TH, acting on mH.

d. the tension force, TC, acting on mC. Do not use the tension value from part c!

e. the fraction TC/TH.     (What should this ratio be if your data was perfect?)

6. For your TC/TH values, calculate the average, standard deviation, and percent error between your average and the accepted value.

7. Make a single scatter plot showing the cart’s acceleration vs. the net force on the cart. Use three data series: 1) first four trials, 2) heavy cart, and 3) tilted track.

8. Add a linear trend line to each data set. For each trend line, use “Set Intercept” with a value of zero. Display the equation for each trend line.   (When the net force is zero, the acceleration had better be zero. Thus, the y-intercept should be 0 m/s2.)

A parallel plate capacitor with adjustible plate separation d and adjustible area A is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V Volts. (C is the capacitance and U is the stored energy.) Give all correct answers concerning a parallel-plate capacitor charged by a battery (e.g. B, AC, CDF).

A) After being disconnected from the battery, increasing the area A will increase C.
B) With the capacitor connected to the battery, increasing the area A will decrease U.
C) With the capacitor connected to the battery, increasing d increases U.
D) With the capacitor connected to the battery, increasing the area A will increase Q.
E) After being disconnected from the battery, increasing d increases V.
F) With the capacitor connected to the battery, increasing d increases C.

(Show all the steps please)

Rotational Dynamics: Four objects of equal mass start at the top of an inclined plane. A solid cylinder, a thin walled cylinder, a solid sphere, and a thin walled sphere. All objects start at rest. Starting at rest,

A) Write down the work energy theorem including both kinetic energy terms and all potential energy terms.

B) If all four objects are released at the same moment, how long does each take to reach the bottom of the incline plane?

C) Find the ratio of translational (linear) kinetic energy to rotational kinetic energy for each object.

D) Compare the results of the race obtained in part a to the results obtained in part b.

E) If the ramp is 20 m long and inclined at an angle od 20 degrees, what is the angular speed of the solid cylinder at the bottom of the ramp.

F) What torque is required to achieve this final angular speed?

(1) Imagine that we have an electron traveling due west from the capitol of the united states steps. It is traveling at 98.94% of the speed of light.

(a) What is the force on the electron from the magnetic field?

(b) What is the radius of curvature of the path that it follows?

(c) What would the answers to parts (a)-(c) be for a proton?

A 6.61-mm-high firefly sits on the axis of, and 14.1 cm in front of, the thin lens A, whose focal length is 5.21 cm. Behind lens A there is another thin lens, lens B, with focal length 21.1 cm. The two lenses share a common axis and are 60.3 cm apart. Is the image of the firefly that lens B forms real or virtual?

How far from lens B is this image located (expressed as a positive number)?

What is the height of this image (as a positive number)? Is this image upright or inverted with respect to the firefly?

A 175 g mass attached to a horizontal spring oscillates at a frequency of 2.80 Hz. At t =0s, the mass is at x= 7.00 cm and has vx =− 35.0 cm/s . Determine:

The maximum speed.

The maximum acceleration.

The total energy.

The position at t= 2.80 s .

In the previous parts, the following was found: period = 0.357 s, angular frequency = 17.59 rad/s, amplitude = 7.277 cm, phase constant = 15.8679 degrees.

Fluid Mechanics: A water tank is a cylinder 4 m in height and 2 meters in diameter. The tank is full at time t_o. The tank sits on a platform 12 m tall. A water tap is located at the bottom center of the tank. The tap, when actuated, opens to a pipe 5 cm in radius.

a.       Write down Bernoulli’s equation. Identify the Pressure, Kinetic and Potential Energy terms. Show that each has the units of an energy density (Joules/Volume).

b.       Use Bernoulli’s equation to compare the difference in pressure between the surface of the water and the bottom of the tank near the edge? Assume the fluid is motionless near the edge.

c.       When a tap is opened water rushes in to a pipe 5 cm in radius. The pipe is straight and drops 12 m to ground level, but along the way slowly in radius to 2 cm. What is the speed of the water as it emerges from the pipe?

d.       Use the continuity equation to find the speed of the water as it enters the pipe 12 m above, i.e. bottom of the tank.

e.       What is the volume and mass flow rate of the stream of water?

f.        What is the pressure of the fluid as it enters the pipe, again at the bottom of the tank.

Suppose a certain laser can provide 140 TW of power in 0.96 ns pulses at a wavelength of 0.25 ?m. How much energy is contained in joules in a single pulse?

I will give 5 stars for the correct answer

Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates: (1) 0.310 kg , ( 0.200 m , 0.310 m ); (2) 0.410 kg , ( 0.110 m , -0.380 m );(3) 0.210 kg , ( -0.290 m , 0.630 m ).

Part A

Find the x-coordinate of the center of mass of the system of three chocolate blocks.

Part B

Find the y-coordinate of the center of mass of the system of three chocolate blocks.

At time =0, a proton is at rest at location <4.7, 1.8, 0> x 10^-6m. An electron is at <2.9,8.7,0> x 10^-6 m. and is moving with a momentum of <3.6,-7.8,0> x 10^-27 kg*m/s. the proton and electron are in outer space, far from any other matter. The proton has a charge of 1.6 x 10^-19 C, and the elctrons charge is exactly the negative of this value.

A.) what is the magnitude of the gravitational force on the electron by the proton?

B.) what is the magnitude of the electric force on the electron by the proton. By what factor is it larger than the gravitational force?

C.) what is the electric force vector on the electron by the proton?

D.) after time 2.0 x 10^-10 s, what is the momentum of the electron?

1) identify the processes that shape planetary surfaces and identify the most common planetary process

2) identify the processes that have taken place on the surface of Mars and Venus.

3) identify the surface processes that have taken place on the surface of Mercury the Moon and the moon's of Jupiter.

What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.7, 128.1, and 129.2 Hz? (Give your answers from smallest to largest.)
Hz
Hz
Hz

1) describe how temperature influenced what materials condensed from the nebular cloud.

2) compare and contrast the composition of the inner and outer planets

3) explain the frost line and the influence it has on the formation of planets (in any solar system).

4) explain why our solar system has rocky inner planets and gaseous outer planets and identify the most metal-rich planet in the solar system

5) explain the occurrence of Hot Jupiters

An electron is accelerated inside a parallel plate capacitor. The electron leaves the negative plate with a negligible initial velocity and then after the acceleration it hits the positive plate with a final velocity β. The distance between the plates is 16.5 cm, and the voltage difference is 149 kV. Determine the final velocity β of the electron using classical mechanics. (The rest mass of the electron is 9.11×10^-31 kg, the rest energy of the electron is 511 keV.)

What is the final velocity β of the electron if you use relativistic mechanics?

a.) Is the acceleration due to gravity a constant or will it vary from place to place on Earth?

b.) What about on another planet or moon?

c.) How does Newton's second law of motion compare to Universal Gravitation?