A mass m = 85 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 18.9 m and finally a flat straight section at the same height as the center of the loop (18.9 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.)

1)

What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track?

m/s

2)

What height above the ground must the mass begin to make it around the loop-the-loop?

m

3)

If the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop?

m/s

4)

If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.9 m off the ground)?

m/s

5)

Now a spring with spring constant k = 18200 N/m is used on the final flat surface to stop the mass. How far does the spring compress?

m

6)

It turns out the engineers designing the loop-the-loop didn’t really know physics – when they made the ride, the first drop was only as high as the top of the loop-the-loop. To account for the mistake, they decided to give the mass an initial velocity right at the beginning.

How fast do they need to push the mass at the beginning (now at a height equal to the top of the loop-the-loop) to get the mass around the loop-the-loop without falling off the track?

m/s

7)

The work done by the normal force on the mass (during the initial fall) is:

positive

zero

negative

An atom is in a time independent one-dimensional potential well. The system's spatial wave function at t=0 is Ψ(x,0) = Ax(a-x) for 0<x<a and zero for all other x. (a) The system's energy is measured at t=0. What is the most likely outcome? Find the probability for obtaining this result. (b) What is the systems's average energy at t=0? Compare it with the energy in (a) and explain your answer.

A -10.0 nC point charge and a +20.0nC point charge are 13.5 cm apart on the x-axis.

Part A

What is the electric potential at the point on the x-axis where the electric field is zero?

Express your answer with the appropriate units.

Part B

What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

Express your answer with the appropriate units.

How much thermal energy (in kcal) is required to change a 48 g ice cube from a solid at - 14.6 oC to steam at 10.8 oC above boiling?

Charges 3 micro coulombs and -6 micro coulombs are placed 5cm from each other. Find where the electric field equals 0 and where the electric potential is zero

Two narrow slits 60 μm apart are illuminated with light of wavelength 500nm. The light shines on a screen 1.2 m distant. How far is this fringe from the center of the pattern?

A certain super capacitor has a capacitance of 1.0F. The maximum voltage is 2.7 V. It is contained in a 8.00mm diameter can that is 13.00 mm long. It has two leads that are 3.50mm apart. It costs $0.29 when bought in bulk. How can such a large capacitance be made in a small container? The largest dielectric constant for oils is about 90. The largest dielectric constant is about 100,000 in material that costs $100,000/kg. Just describe the type of design (vacuum parallel-plate, dielectric parallel-plate, cylindrical, dielectric cylindrical, rolled parallel-plate, electrolytic, adjustable plate, etc.)

What is the energy density of the capacitor when fully charged?

A skier is skiing downhill at constant speed. The slope is inclined at 10^o with respect to the horizontal. The skier’s mass is 65 kg, what is the value of the coefficient of kinetic friction between the skis and the snow?

The Human Eye THE HUMAN EYE: While digital camera form images with pixels, the human eye forms images with rods and cones that lie on the retina. If two point objects close together are to be seen as two distinct objects, the images must fall on the retina on two different cones that are not adjacent. That is, there must be a cone between them. Assume that the cones are sensitive to a wavelength of 550nm. If the iris is about 5mm in diameter, and we can model the human eye as a sphere with roughly a 25mm diameter,

a. What is the minimum separation between two objects at a distance of 2rn away from the eye that we can resolve at this wavelength?

b. What is the distance between the two cones on the retina?

How does rotational inertia play a role when a quarterback throws a ball so that it spirals in flight? What about a figure skater spinning about her axis of symmetry with her arms outstretched and then pulling them in tight to her body?

Let's return to Interstates 80 and 680 in rural Iowa, courtesy of Google Earth. (Open Google Earth using the same file as in the Pre-Lab, Interstate_80_in_Iowa.kmz. (Do it the same way you did in the Chapter 1 lab. If you are using Chrome, there should be a button for this file in the lower left corner of your screen after you download it. If you are using other browsers, this file is probably in your Downloads folder.)
Starting from a complete stop, a car gets on I-80 at the I-80 and I-680 interchange, then drives to Stuart and continues east. After starting to move, the car accelerates over a distance of 1/4 mile, until reaching 55 miles per hour and continuing to Stuart at that constant speed. So between the I-680 interchange and Stuart, the time and distance can be considered to be composed of two time/distance parts:

(link) Interstate_80_in_Iowa.kmz (Google maps shows it is 65.5 miles from I680 to stuart)

time(1): the time taken accelerating from 0 mph to 55 mph during the first 1/4 mile

distance(1): the first 1/4 mile over which the car was accelerating

time(2) the time taken to cover the rest of the distance to Stuart going at the constant speed 55 mph

distance(2): the rest of the distance to Stuart after the 1st 1/4 mile

5.A. What is distance(2), the distance to Staurt after the 1^st ¼ mile? _______________

5.B.   What is the time time(1) spent accelerating, in units of hours?___________

5.C. What is the time time(2) spent driving at the constant speed after the 1^st ¼ mile to Stuart? ____________

5.D. - What percentage of the total distance of the trip (distance(1) + distance(2)) between I-680 interchange and Stuart was spent accelerating?

5.E.   What percentage of the total time of this trip (time(1) + time(2)) was spent accelerating?

4. In the comics and movies, the Incredible Hulk often travels great distances by making huge leaps. According to Marvel.com, the Hulk is capable of leaping a horizontal distance of up to three miles (4.28 km) in a single leap.

a. What initial angle should the hulk jump at if he wants to maximize his horizontal distance?

b. What initial velocity must the Hulk jump with if he is going to reach a horizontal distance of 4.28 km.

c. What is the maximum height reached by the hulk during this jump.

d. When Hulk is at the maximum height, what is the magnitude and direction of his velocity?

The inventory consist of

Xo - x initial

X - x final

Vo - velocity initial

V - velocity final

a - accelerate

t - time

E=1/2 CV^2 E= 1/2 (164 microF) (10^-6 F) (119 V)^2 E= 1.168 J How do you figure out the J from the F V^2   

A) A common practice for a person with a high fever is to take a bath in cool water. Assuming an 80 kg person is really ill and needs to cool down from 40°C to 37°C. What is the minimum amount of water needed for bathing assuming the water begins at room temperature, 25°C? The specific heat of the body on average is 3470 J/kg°C and water is 4186 J/kg°C. 17.

b) Students want to impress their physics teacher by writing an essay which describes the heating of ice at a temperature below 0°C to steam at a temperature above 100°C. Write such a paragraph using the terms energy, temperature, and phase change. Be sure to include a description of the five major stages.