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

9. 2 kg glider is traveling toward the right with a speed of 1 m/s on an air track. A 3 kg glider is traveling on the same track to the left at 2 m/s. If they collide and stick together what speed will they move with?

10. A car with a mass of 1000 kg is stopped at a stop sign. The car accelerates to 20 m/s in 5 seconds. (a) What is the magnitude of the acceleration of the car during those 5 seconds? (b) How far does the car travel during those 5 seconds? (c) What is the magnitude of net force on the car while it is accelerating?

11. A skydiver jumps from a plane, 1 second after opening her parachute the resistive force on her has a magnitude of 1200 N. If the skydiver has a weight of 800 N (and therefore a mass of 80 kg), what are the magnitude and direction of her acceleration?

12. A compact car with a mass of 1200 kg traveling at 20 m/s hits a stationary SUV. The SUV has a mass of 2400 kg. (a) Which vehicle experiences the greater force of impact? Explain your answer. (b) Which vehicle has a greater acceleration during the collision? Explain your answer. (c) Explain what additional information is needed to determine the average force on the compact car during the collision.

13. You throw a ball into the air. At its highest point it comes to rest, is it in equilibrium? Explain.

A 1.00 kg , horizontal, uniform tray is attached to a vertical ideal spring of force constant 195 N/m and a 285 g metal ball is in the tray. The spring is below the tray, so it can oscillate up-and-down. The tray is then pushed down 12.1 cm below its equilibrium point (call this point A) and released from rest.

a) How high above point A will the tray be when the metal ball leaves the tray?

b) How much time elapses between releasing the system at point A and the ball leaving the tray?

c) How fast is the ball moving just as it leaves the tray?

Two manned satellites approaching one another at a relative speed of 0.150 m/s intend to dock. The first has a mass of 4.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity? Adopt the reference frame in which the second satellite is initially at rest and assume that the positive direction is directed from the second satellite towards the first satellite.

m/s

A 1.00-cm-high object is placed 3.95 cm to the left of a converging lens of focal length 9.00 cm. A diverging lens of focal length −16.00 cm is 6.00 cm to the right of the converging lens. Find the position and height of the final image.

On a frictionless horizontal air table, puck A (with mass 0.245 kg ) is moving toward puck B (with mass 0.373 kg ), which is initially at rest. After the collision, puck A has velocity 0.118 m/s to the left, and puck B has velocity 0.647 m/s to the right.

a. What was the speed vAi of puck A before the collision?

b. Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

A pendulum clock has a heavy bob supported on a very thin steel rod that is 1.00000 m long at 21.0 ∘C.

a)To 6 significant figures, what is the clock's period? Assume that g is 9.80 m/s2 exactly.

b)To 6 significant figures, what is the clock's period if the temperature increases by 13.0 ∘C? Assume that coefficient of linear expansion of steel is 1.20×10−5 K−1 .

c)The clock keeps perfect time at 21.0 ∘C. At 34.0 ∘C after how many hours will the clock be off by 1.00 s ?