An 82.0 kg skydiver jumps out of a balloon at an altitude of 1 100 m and opens the parachute at an altitude of 160 m.

(a) Assuming that the total retarding force on the diver is constant at 60.0 N with the parachute closed and constant at 3 600 N with the parachute open, what is the speed of the diver when he lands on the ground?

(b) Do you think the sky diver will be injured? Explain.

(c) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00 m/s?m

(d) How realistic is the assumption that the total retarding force is constant? Explain your answer.

A pumpkin of mass 5kg shot out of a student-made cannon under air pressure at an elevation of 45 degrees fell at a distance 142m from the cannon. The students used light beams and photocells to measure the initial velocity of 54m/s. If the resistive force was F = -kmv^2, what was the value of k?

Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off before much of it accumulates. The electric field around the needle is much larger than the field around the body of the airplane and can become large enough to produce dielectric breakdown of the air, discharging the airplane. To model this process, assume that two charged spherical conductors are connected by a long conducting wire and a charge of 79.0 µC is placed on the combination. One sphere, representing the body of the airplane, has a radius of 6.00 m, and the other, representing the tip of the needle, has a radius of 2.00 cm.

(a) What is the electric potential of each sphere? r = 6.00 m: ]V

r = 2.00 cm: V

(b) What is the electric field at the surface of each sphere?

r = 6.00 m: magnitude____________ V/m? direction_________?

r = 2.00 cm: magnitude ____________ V/m? direction________?

Show that the charges placed on a system of fixed conductors are distributed on the conductors' surfaces in such a way that the electrostatic energy of the resulting field is a minimum (Thomson theorem)

1. Use the kinematic equation, d_f = ½ at², to calculate the acceleration of each object in Table 1. Record the calculated acceleration in Table 1.

2.    Show a sample calculation:

3. Answer all of the Post-Lab Questions (Note: Information to help with these questions may be available in the Gravity Lab Introduction)

1. How does the rate of acceleration you calculated for each object compare? Are they similar or different? Why?

2. The acceleration due to gravity calculated this way works well for objects near the Earth’s surface. How would you have to change the equation if the object was 100,000 meters above the ground?

3. How does air resistance alter the way we perceive falling objects?

4. Is the force acting on a massive object larger than that acting on a less massive one? How can you verify this without taking any measurements?

Find the lowest two "threefold degenerate excited states" of the three-dimensional infinite square well potential for a cubical "box." Express your answers in terms of the three quantum numbers (n1, n2, n3). Express the energy of the two excited degenerate states that you found as a multiple of the ground state (1,1,1) energy. Would these degeneracies be "broken" if the box was not cubical? Explain your answer with an example!

The displacement vectors A and B shown in the figure below both have magnitudes of 2.50 m. The direction of vector A is θ = 35.5°. (a) Find A + B graphically. magnitude m direction ° counterclockwise from the +x axis (b) Find A − B graphically. magnitude m direction ° counterclockwise from the +x axis (c) Find B − A graphically. magnitude m direction ° counterclockwise from the +x axis (d) Find A − 2B graphically. magnitude m direction ° counterclockwise from the +x axis

A student sits on a rotating stool holding two 2.2-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg · m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.46 m from the rotation axis. (a) Find the new angular speed of the student. (b) Find the kinetic energy of the student before and after the objects are pulled in. before after (c) Where does the energy difference come from/go to?

2. Vertical jumping performance is often used as a crude measurement of muscle power. Considering the various deterministic factors of jumping performance, which factor or sub-height is most closely related to vigorous muscular effort? In consideration of your answer, which method of estimating flight height is probably most appropriate? Explain

A parallel plate air capacitor with no dielectric between the plates is connected to a constant voltage source. How would the capacitance and the charge change if a dielectric of dielectric constant K=2 is inserted between the plates. C0 and Q0 are the capacitance and charge of the capacitor before the introduction of the dielectric.

A Freight truck is driving down I-95 at 70 mph.

a. Assuming the truck is driving through calm air, what is the pressure that is exerted on its frontal area when cruising at that speed? Make necessary simplifying assumptions.

b. How many pounds of force are experienced by the front of the truck assuming its frontal area is flat and 13 ft by 8 ft?

c. In full-scale wind tunnels, engineers recreate wind flow in driving conditions to understand how their designs would fare in the real world. What wind speeds are typically reached in wind tunnels? Cite your sources.

d. What power from the truck’s motor is needed to overcome this force?

Extra credit: What is the ultimate thermodynamic effect of propelling the truck for one mile over level terrain?

4. A physics student throws two bricks from the top of Fawcett Hall. Brick A is thrown straight up with an initial speed vo, and brick B is thrown straight down with the same initial speed. If air resistance is negligible, when they strike the ground

      a) B has greater speed.      b) A has greater acceleration.      c) B has greater acceleration.

      d) A and B have same speed.      e) A has greater speed.

5. A bullet shot straight up returns to its starting point in 10 s. If it moved frictionlessly, its initial speed must have been _____ m/s.

      a) 24.5       b) 9.8        c) 49         d) 196        e) 98

6. A butterfly moves with a speed of v = 12.0 m/s. The x-component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x-axis must be

      a) 48.2°      b) 41.8°      c) 53.0°      d) 33.7°      e) 30.0°

7. Two displacement vectors have magnitudes of 5 m and 7 m, respectively. When these two vectors are added, the magnitude of the sum is

      a) between 2 m and 12 m.      b) larger than 12 m.      c) 12 m.      d) 2 m.

      e) smaller than 2.

8. A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. Its initial speed was _____ m/s.

      a) 8.13       b) 13.1       c) 39.8       d) 7.35       e) 12.5

9. You hit a tennis ball over the net. When the ball reaches its maximum height, its speed is

      a) greater than its initial speed.      b) less than its initial speed.

      c) equal to its initial speed.      d) zero.

A catapult launches a rocket at an angle of 49.6° above the horizontal with an initial speed of 112 m/s. The rocket engine immediately starts a burn, and for 3.58 s the rocket moves along its initial line of motion with an acceleration of 32.5 m/s². Then its engine fails, and the rocket proceeds to move in free-fall.

(a) Find the maximum altitude reached by the rocket.
m
(b) Find its total time of flight.
s
(c) Find its horizontal range.
m

An explorer starts hiking from base camp 2 mi north, then he walks for a while in a direction 30 degrees east of north, then he walks 4 mi in a direction 60 degrees south of east, finally, he walks in a direction 12.62 degrees south of west back to base camp. Determine the magnitudes of his second and fourth displacement.