The length of nylon rope from which a mountain climber is suspended has a force constant of 1.18 ✕ 10⁴ N/m.

A) What is the frequency (in Hz) at which he bounces, given that his mass plus the mass of his equipment is 78.0 kg?

B) How much would this rope stretch (in cm) to break the climber's fall if he free-falls 2.00 m before the rope runs out of slack? Hint: Use conservation of energy.

C) Repeat both parts of this problem in the situation where twice this length of nylon rope is used.

frequency (in Hz)

stretch length (in cm)

For wavelengths of two lines in a vacuum measuring 3033.71 and 3033.75 angstroms.

(a) Calculate the frequency for both wavelengths

(b) calculate the index of refraction for air (at the frequency of the lower wavelength.

(c) A light source emits only at the lower wavelength (3033.71 angstroms) and is directed into a Michelson interferometer. If the moving mirror in the interferometer travels at a velocity of 0.15cm/sec and moves a total distance of 0.40 cm what would the resulting interferogram look like? sketch intensity vs retardation that would be obtained.

(d) Calculate the frequency of the resulting interferogram

(e) Would this interferometer be able to "barely resolve" the two emission lines at 3033.71 and 3033.75 angstroms?

What is the theory of relativity?

1. A rectangular lamina has vertices (0,0), (0,2), (3,0), (3,2) and density σ = xy (in kg/m²). Find a) the mass M of the lamina b) x_CM and c) y_CM. (Answers: a) M = 9 kg, b) x_CM = 2 m, c) y_CM = 4/3 m)

Two resistors have resistances R(smaller) and R(larger), where R(smaller) < R(larger). When the resistors are connected in series to a 12.0-V battery, the current from the battery is 1.48 A. When the resistors are connected in parallel to the battery, the total current from the battery is 10.9 A. Determine the two resistances. R(smaller)= R(larger)=

The coordinates of an object moving in the xy plane vary with time according to the equations x = −5.08 sin ωt and y = 4.00 − 5.08 cos ωt, where ω is a constant, x and y are in meters, and t is in seconds.

(a) Determine the components of velocity of the object at t = 0. (Use the following as necessary: ω.) v with arrow = m/s

(b) Determine the components of the acceleration of the object at t = 0. (Use the following as necessary: ω.) a with arrow = m/s2

(c) Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t > 0. (Use the following as necessary: omega for ω and t.) r with arrow = m v with arrow = m/s a with arrow = m/s2

(d) Describe the path of the object in an xy plot.

Compare a nova to a Type I supernova to a Type II supernova. What do these three objects have in common? How are these three objects different?

A large wooden turntable in the shape of a flat disk has a radius of 2.45 m and a total mass of 140 kg . The turntable is initially rotating at 3.20 rad/s about a vertical axis through its center. Suddenly, a 68.5 kg parachutist makes a soft landing on the turntable at a point on its outer edge.

Find the angular speed of the turntable after the parachutist lands.(Assume that you can treat the parachutist as a particle.)

While prepping to start an internship at the local hospital you learn that systemic arteries have diameters greater than 10 mm. You know that blood carries charged particles, and you start to wonder how strong a uniform magnetic field would have to be in order to detect the flow of these charges in the blood with a voltmeter that can measure voltage differences down to a millivolt. You assume that the blood flows at a rate of about 10 cm/s

The emissivity of the human skin is 97.0 percent. Use 35.0 °C for the skin temperature and approximate the human body by a rectangular block with a height of 1.57 m, a width of 41.5 cm and a length of 21.0 cm. Calculate the power emitted by the human body.

Fortunately our environment radiates too. The human body absorbs this radiation with an absorbance of 97.0 percent, so we don't lose our internal energy so quickly. How much power do we absorb when we are in a room where the temperature is 22.0 °C?

How much energy does our body lose in one second?

You are testing a new t-shirt cannon. You decide to fire the t-shirts vertically straight up in the air so that you do not have to walk to pick up the launched t-shirts. First, a green t-shirt is launched vertically upwards with a speed of 12 m/s. Exactly 1.0 s later, a blue t-shirt is launched vertically upwards with a speed of 18 m/s. At what time (after the launch of the first green t-shirt) will the two shirts collide, and at what height above the cannon? You may ignore air resistance throughout the problem.

Good old Florida! As an alum of UCF, you also plan to use an off-grid power system. While you absolutely adore four-wheel drive, you bought a plug-in hybrid car, for cost efficiency. Estimate the number of excess solar panels you would need to add to your off-grid power system in order to keep your car charged up without ever burning a drop of gasoline.

4. The SI unit of electric charge is the coulomb, C, is equivalent to the charge on 6.242⨯1018 protons. Express amps and ohms in terms of the base SI units of J, C, and s. Use dimensional analysis and Ohm’s Law to show that volts may be expressed as J/C. (2 points)