A 23.0-kg child on a 4.00-m-long swing is released from rest when the ropes of the swing make an angle of 25.0° with the vertical. (a) Neglecting friction, find the child's speed at the lowest position. m/s (b) If the actual speed of the child at the lowest position is 2.40 m/s, what is the mechanical energy lost due to friction? J

In class, you have seen how to calculate the maximum speed for a car to go around a flat curve (with friction), and for a banked curve (without friction). Here, you will consider the general case. (For each question part below, include a free-body diagram.) a) (3 points) Explain briefly why the car can go around the banked curve safely even without friction, and why that is not the case for the flat curve. b) (5 points) Now consider a curve that is banked so that a car can safely take it at a speed of 85 km/h, even if there were no friction. Assuming the radius of the curve is 68 m, calculate the angle at which it has been built. c) (6 points) For the banked curve, calculate the maximum speed that a car can have to safely go through it if the coefficient of static friction is 0.3. What will happen if the car is faster? d) (6 points) For the same curve, calculate the minimum speed the car must have to safely make it through. What will happen if the car is slower?

A sinusoidal electromagnetic wave of frequency 6.10

1. A nuclear power plant has an overall efficiency of 31% and a power output of 800MW. For one year operating at full capacity, calculate a) the number of joules produced; b) the number of fission events that were required to produce those joules; c) the mass of uranium oxide (UO₂) that has been used in fission; and d) the market cost of that uranium oxide if it was all high quality.

Is there any electric field inside a perfect conductor? Is there any conduction current inside a perfect conductor? Can static magnetic fields exist in a perfect conductor?

A charge of 2.20 µC is uniformly distributed on a ring of radius 9.0 cm. Find the electric field strength on the axis at the following locations.

(a) 1.2 cm from the center of the ring
N/C

(b) 3.9 cm from the center of the ring
N/C

(c) 4.0 m from the center of the ring
N/C

(d) Find the field strength at 4.0 m using the approximation that the ring is a point charge at the origin.
N/C

(e) Compare your results for parts (c) and (d) by finding the ratio of the approximation to the exact result.


(f) Is your approximation result a good one? Explain your answer. (Do this on paper. Your instructor may ask you to turn in your work.)

A doppler meter of frequency 3 MHz (accurate to +/ - 10 Hz) is used to monitor the heart rate of a fetus in early pregnancy (8 – 10 weeks). Determine the maximum positive and negative shift in ultrasound frequency detected by the meter due to the heart motion. For a simplified model, take the main fetal heart muscle to move like a mass on a spring undergoing Simple Harmonic Motion, with a maximum distance (amplitude) x max = A = 1.0 mm and a frequency, f = 150 beats/min. Take the speed of ultrasound in the body to be v =1540 m/s. Method: write a sine function that describes the motion of the heart muscle. 2.determine the maximum positive and negative velocity of the heart muscle by differentiating your equation 3.use the doppler equation to determine the corresponding frequency shifts.

Chickens having a mass of 5 kg are immersion frozen in propylene glycol at -30°C (ρ=1068 kg/m^3). If the volume of each vacuum packaged bird is about 6000 cm^3, what force must be applied to each bird to keep it at mid-depth in the 1-m deep tank?

A proton moves through a uniform magnetic field given by  B→=(5.52i^−10.0j^+20.9k^) mT. At time t₁, the proton has a velocity given by   v→=vxi^+vyj^+(2.19⁢  km/s)k^ and the magnetic force on the proton is   F→B=(3.69×10−17⁢ N)i^+(2.03×10−17⁢ N)j^ . (a) At that instant, what is v_x? (b) At that instant, what is v_y?

(a) _ m/s

(b) _ m/s

In the last lab, we learned how an AC electromagnetic field can produce circulating eddy currents within a bulk conductor, such as a ferromagnetic core inside a coil. These eddy currents require energy to produce, and therefore cause efficiency losses in some devices. How do we reduce eddy current losses in transformers?

A 5.00 kg lead sphere is dropped from the top of a 60.0-m-tall building.

Part A

If all of its kinetic energy is converted into heat when it hits the sidewalk, how much will its temperature rise? (Ignore air resistance.)

Express your answer in degrees celsius to three significant figures.

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6. A water slide can be considered to be frictionless. The top of the slide is 4.2 m above the bottom of the slide. Riders exit the slide with a horizontal velocity. The bottom of the slide is 1.5 m above the water. A certain rider has a mass of 27 kg.

A. Sketch the situation at the top of the slide, bottom if the slide, and just before they hit the water.

B. What is their gravitational potential energy at the top of the slide, relative to the bottom of the slide and relative to the top of the water?

C. What is their kinetic energy and speed at the bottom of the slide?

D. How far do they travel horizontally from the bottom of the slide before they hit the water?

E. Does the horizontal distance traveled depend on the mass of the rider? Explain.

1.20cm tall object is 50.0cm to the left of a diverging lens (lens 1) of focal length of magnitude 40.0cm. A second converging lens (lens 2) of focal length 60.0cm, is located 300cm to the right of the first lens along the same optic axis.

(a)Calculate the location of the image (call it I1) formed by the lens1.

(b) Is image I1 real or virtual?

(c) Is image I1 on left side or right side of lens 1?

(d) Calculate magnification m1 of lens 1. Is image I1 upright or inverted?

(e) Calculate height of the image I1.

(f) I1 is now the object for the second lens. Is the object for lens 2 real or virtual?

(g) Calculate the object distance for lens 2?

(h) Calculate the location of the image I2 produced by lens2.

(i) Calculate magnification m2 of lens2. Is image I2 upright or inverted?

(j) Calculate height of the image I2.

(k) Find overall magnification of these two lens system.

(l) Is final image real or virtual?

(m) Is final image upright or inverted, relative to initial object?

(n) Is final image enlarged or reduced in size, relative to initial object?

(o) Draw a diagram showing location of lenses, objects and images

A 1300-kg rocket has a net propulsion force of 60 kN (kiloNewtons). Over a short time period, it uniformly speeds up from an initial velocity of 40 m/s to a final velocity of 55 m/s. Assume that the mass of the rocket is constant during this time period and that the net force is along the direction of motion.

A) What is the change in speed of the rocket in m/s and in mph?
m/s
mph

B) What is the magnitude of the impulse delivered to the rocket during this time period?
kg*m/s

c) How long did it take for the rocket to speed up from 40 m/s to 55 m/s?
s

D) What is the magnitude of the acceleration of the rocket?
m/s²

E) What are the initial and final kinetic energies of the rocket in kilojoules (kJ)?
KE initial:  kJ
KE final:  kJ

F) What is the net work done on the rocket in kilojoules (kJ)?
kJ

G) How far did the rocket travel during this time period?

in a similar setup to the equilibrium lab, you place the fulcrum at the 25 cm mark on a uniform meter stick with mass 150g. Then you hang a mass #1 of 75 grams at the 62.5 mark, a mass #2 of 25 grams at the 12.5 cm mark, and an unknown mass #3 at the 0 cm mark. Draw a free body diagram and find the value of mass #3 in order for the system to be in equilibrium