1. If you are given an equipotential diagram, how could you use it to figure out the direction of the electric field at a specific location? Explain your thinking in detail, using both words and a picture.

2. If you are given an equipotential diagram, how could you use it to figure out which regions have a stronger electric field and which regions have a weaker electric field? Explain your thinking in detail, using both words and a picture.

In the shot put, a heavy lead weight—the "shot"—is given an initial velocity, starting from an initial elevation approximately equal to the shot putter's height, say, 2.00 m. If v₀ = 7.90 m/s, find the horizontal distance traveled by the shot for the following initial angles above the horizontal. (a) θ₀ = 0°


(b) θ₀ = 40.0°


(c) θ₀ = 45.0°

A concave spherical mirror with a focal length of 12 cm faces a plane mirror with the optical axis of the spherical mirror perpendicular to the plane mirror. A small object is placed at point P on the optical axis, 11 cm from the plane mirror and 29 cm from the vertex of the spherical mirror. Find the distance from the plane mirror to the three nearest images. (Enter your answers from smallest to largest.)

An astronaut finds herself in a predicament in which she has become untethered from her shuttle. She figures that she could get back to her shuttle by throwing one of three objects she possesses in the opposite direction of the shuttle. The masses of the objects are 5.4 kg, 7.9 kg, and 10.1 kg, respectively. She is able to throw the first object with a speed of 15.00 m/s, the second with a speed of 10.6 m/s, and the third with a speed of 5.5 m/s. If the mass of the astronaut and her remaining gear is 75.0 kg, determine the final speed of the astronaut with respect to the shuttle if she were to throw each object successively, starting with the least massive and ending with the most massive. Assume that the speeds described are those measured in the rest frame of the astronaut.

At each position in a 3D grid lies an atom with a positive or negative spin, specified by values +1 and -1, respectively. The spin value at each position is assigned randomly based on whether a randomly generated number is greater than or less than 0.5. I need to plot a 3D visualization of this grid using MATLAB in which positive spin locations are represented by markers of one color and negative spin locations are another color.

A platinum sphere with radius 0.0115 m is totally immersed in mercury. Find the weight of the sphere, the buoyant force acting on the sphere, and the sphere\'s apparent weight. The densities of platinum and mercury are 2.14

A boy tosses a football upward. If the football rises a vertical distance of 6.9m and the boy catches it at the same point he released it, what is the velocity of the ball just before he catches it? (Assume upward is the positive direction. )

A car accelerates uniformly from rest and reaches a speed of 23.0 m/s in 8.96 s. Assume the diameter of a tire is 57.9 cm.

(a) Find the number of revolutions the tire makes during this motion, assuming that no slipping occurs.
   

(b) What is the final angular speed of a tire in revolutions per second?
rev/s

An individual is nearsighted; his near point is 12.0 cm and his far point is 51.0 cm.

(a) What lens power is needed to correct his nearsightedness?

[answer] diopters

(b) When the lenses are in use, what is this person's near point?

[answer] cm

A: A bird watcher meanders through the woods, walking 0.30 km due east, 0.80 km due south, and 2.30 km in a direction 45.0° north of west. The time required for this trip is 4.00 h.

(a) Determine the magnitude and direction (relative to due west) of the bird watcher's displacement. Use kilometers and hours for distance and time, respectively.

(b) Determine the magnitude and direction (relative to due west) of the bird watcher's average velocity.

B: An airplane is flying with a velocity of 226 m/s at an angle of 30.0° with the horizontal, as the drawing shows. When the altitude of the plane is 2.1 km, a flare is released from the plane. The flare hits the target on the ground. What is the angle θ?

C: After leaving the end of a ski ramp, a ski jumper lands downhill at a point that is displaced 33 m horizontally from the end of the ramp. His velocity, just before landing, is 18.5 m/s and points in a direction 43° below the horizontal. Neglecting air resistance and any lift he experiences while airborne, find his initial velocity (magnitude and direction), when the he left the end of the ramp.

1.45 kg    of ice at   -5 ∘C    is dropped into   31 kg    of water at temperature   15.3 ∘C   .

Part A - Final Temperature

What is the final temperature of the system? (If I've set the problem up right, you should be given numbers such that all of the ice has melted.)

Part B - Entropy of Warming Ice

What is the change in entropy of the ice, as it warms up before melting?

Part C - Entropy of Ice Melting

What is the change in entropy of the ice as it melts?

Part D - Entropy of Water From Ice Warming Up

After the ice melts, it's just water, and this water still has to warm up to the final temperature. What is the entropy change of this process?

Part E - Change in Entropy of the Water Cooling

Meanwhile, the initially warm water is cooling down. What is the entropy change of this water, which is undergoing cooling?

Part F

What is the total change in the entropy of the system?

A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.81 V and a current of 3.8 A are induced in the coil. The wire is then re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What (a) emf and (b) current are induced in the square coil?

A 89.35-kg skier with an initial speed of v_i=43.91 m/s coasts up a H=15.58-m-high rise as shown in the figure. The slope angle is theta=50.33. What is her final speed at the top? Assume the coefficient of friction between her skis and the snow is 0.069 (Hint: Find the distance traveled up the incline assuming a straight-line path as shown in the figure.) Use g = 10 m/s².

A small circular coil with a radius of 1.00 cm has 20 turns and carries a current. A magnetic field probe is located somewhere along the coil's central axis, much farther from the coil's center than the coil's radius.

A. The probe indicates that the magnetic field points down the axis, towards the center of the coil. Looking down the axis towards the coil, the current must be flowing which way? (clockwise or counterclockwise)

B. At a distance of 3.0 meters from the center of the coil, the probe indicates that the coil's magnetic field has a magnitude of 13.0 pT (10^-12 T). How much current is flowing in the coil?

C.How strong is the field at the center of the coil, in Gauss?

D. If the probe is moved to a distance of 9.0 meters from the center of the probe, how much weaker the magnetic field it detects be?

In laboratory tests, a new construction material was found to conduct heat at a rate of 10.2 Btu’s per hour per square meter of surface area. The temperature on one side of the wall was held at a constant 5 F while the other side was held at 70 F. The test specimen was 12.0 inches thick. What is the ambient air temperature (F) on the warm side of the wall? Assume there is free convection on the warm side of the wall, and the warm side is indoors.