Instructions:

Write the equations that will be used for each problem and include every algebraic process.

A spring oscillates with the angular frequency of 2 radians / seconds. There is a mass of 0.500 kilograms tied to the dock. The pier stretches about 0.08 meters.

a. Determine the mechanical energy of the mass.

b. Determine the velocity of the object when it passes through the point x = 0.02 meters.

A thin, uniform disk with mass M and radius R is pivoted about a fixed point a distance x from the center of mass. The disk rotates around the fixed point, with the axis of rotation perpendicular to the plane of the disk. What is the period as a function of x, M, R, and acceleration due to gravity (g), and what is the distance x that gives the smallest period?

Two astronauts, Hans and Dexter, are on a spacewalk, floating at rest next to their space vehicle. They argue and Hans shoots Dexter with a handgun. The bullet has a mass of 15 grams and a muzzle velocity of 250 m/s. Hans now finds himself drifitng away from the spacecraft.

a. Hans and his spacecraft have a mass of 200kg, how fast is he drifting away?

b. Hans only had one bullet, but he is holding a gun of mass 1.1 kg. How fast must he throw it to stop drifting away from the spacecraft?

c. Meanwhile, on Earth, a solid cylinder of mass 5 kg rolls without slipping toward a hll with a velocity of 5 m/s. How high up the hill will the cylinder roll?

d. The bullet lodges in Dexter, who can be thought of as a long thin rod of length 2 m and mass 200kg. It lodges .8m above his center of mass. What are his linear and angular velocity as he drifts away into space?

A hypodermic needle is 4.0 cm long and has an inner diameter of 0.25 mm. Assume the syringe contents have the same properties as water and is at 20 C. a. What pressure is needed to deliver a steady flow of 0.1 cm3 per second? b. If the inner diameter of the needle were increased by 20%, what pressure would be needed to deliver the same flow?

After the Chernobyl nuclear accident, the Pripyat River in Ukraine received 5.0 ×10¹¹ Bq yr^?1 of ⁹⁰Sr from around the Chernobyl nuclear plant through runoff water and groundwater seepage, totaling 1.0 × 10⁷ m³ yr^?1 of the effluent discharge. The Pripyat River width under a normal (mean annual) flow condition is 200 m. The nearest resident is living at the town of Chernobyl, which is 10 km downstream on the same (south) side of the river as the nuclear plant. Determine the ⁹⁰Sr concentration in the river at the town of Chernobyl.

A wheel turns with a constant angular acceleration of 0.700 rad/s2rad/s2. I JUST NEED PART B , THANK YOU.

part a :

How much time does it take to reach an angular velocity of 6.00 rad/srad/s, starting from rest?

Express your answer in seconds.

Answer=8.57s

part b:

Through how many revolutions does the wheel turn in this interval?

Express your answer as a number of revolutions.

Determine if the following forces are conservative

a.) ? = ? 2??̂+ ? 2??̂+ ????̂

b) ? = ??????̂+ ?????̂+ ???̂

c) ? = ??̂+ ??̂+ ??̂

d) ? = (3? 2?? − 3?)?̂+ (? 3 ? − 3?)?̂+ (? 3? + 2?)?̂

e) ? = −?? where a is a constant.

A puck with a mass m1 = 28.0 g moving at 1.00 m/s approaches a stationary puck with a mass m2 = 102 g on an air table and they undergo a two-dimensional elastic collision. As a result of their interaction, the incident puck moves away with a speed v1 = 0.785 m/s and the other puck moves away with a speed v2 in a different direction. What is the angle between the velocities v1 and v2 ?

Explain please!!!

1. Real heat engines, like the gasoline engine in a car, always have some friction

between their moving parts, although lubricants keep the friction to a minimum. Would a

heat engine with completely frictionless parts be 100% efficient? Why or why not? Does the

answer depend on whether or not the engine runs on the Carnot cycle? Again, why or why

not?

2.Some critics of biological evolution claim that it violates the second law of thermo-

dynamics, since evolution involves simple life forms developing into more complex and more

highly ordered organisms. Explain why this is not a valid arguement against evolution.

14. If the photon is travelling towards earth, from a region with lower gravitation, the shift will be towards a _______ in the wavelength.

a. Increase

b. Decrease

c. No change

d. None of the above

15. Gravitational waves carry energy and momentum, travel at a speed

a. Slower than that of light

b. Faster than that of light

c. Same speed of light

d. None of the above

16. Gama rays can be considered as _____

a. Wave

b. Particles

c. Both particles and waves

d. None of the above

17. By considering the electromagnetic radiations are particles, we can explain the following properties

a. Reflection

b. Refraction

c. Interference

d. Diffraction

18. In Young’s double slit experiments, the central fringe is always

a. Bright

b. Dark

c. Bright or dark depends on the length between screen and slits

d. Bright or dark depends on the length between slits

19. According to Stefan’s law total radiant heat energy emitted from a source is proportional to

a. T4

b. 1/T4

c. T2

d. 1/T2

A spring stretches 4.0cm when a load of 20N suspended. How much will the spring stretch if 50.0N load is suspended from it and it does not reach it's elastic limit?

2. You purchase a 500g sample of gold and want to know if it is pure to see if you were cheated. You found the sample when lowered into water displaced 27.5 ml. Was the sample pure gold?

A toy car starts from rest and accelerates on a straight road at a rate of 3m/s^2 for 5 seconds. In the next 2 seconds, it continues to move at a constant speed. Finally, it accelerates at a rate of 2m/s^2 until it stops in the rest of the rest of the time. Find its

a.) Displacement

b.) Speed at t=6 seconds

c.) plot the following graphs:

I. x vs. t

II. v vs. t

III. a vs. t