A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.46 x 104 rad/s to an angular speed of 3.29 x 104 rad/s. In the process, the bit turns through 3.02 x 104 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 9.56 x 104 rad/s, starting from rest?

A hollow sphere is released from the top of an inclined plane of inclination theta. (a) What should be the minimum coefficient of friction between the plane and the sphere to prevent it from sliding? (b) Find the kinetic energy of the sphere as it moves down a length l on the incline if the friction coefficient is half the value calculated in part (a).

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Find the magnetic field on the z axis at z +8.0 cm if (a) the currents are both in the -x direction and (b) the current in the wire at y -6.0 cm is in the -x direction and the current in the wire at y +6.0 cm is in the +x direction.

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?