3. A rigid uniform disk (moment of inertia I = 1/2 m R²) has a mass m = 10 Kg and radius R = 2 m, it is free to rotate around a fixed axis passing through its center and is at rest at t = 0 s. A constant force F = 20 N is applied halfway between the center and the edge of the disk, in a direction perpendicular to the disk radius.

(i) Calculate the torque, the angular acceleration, the angular velocity and the rotation angle of the disk after t = 10 s. τ=20 Nm ; α=1 s^-2 ; ω=10 s^-1 ; Δθ=50 (rad)

(ii) Calculate the kinetic energy and the angular momentum of the disk at t = 10 s. K=1000 J ; L = 200 Js

(iii) Show that the relationships between torque, work, kinetic energy and angular momentum are numerically satisfied. W = τ∗Δθ = 20 Nm*50 = 1000 J ; Kf-Ki = 1000 J

τ∗Δt = 20 Nm*10s = 200 Js ; Lf-Li = 200 Js

THE ANSWERS ARE IN BOLD, COULD YOU PLEASE SHOW THE WORKING NEEDED FOR THIS QUESTION?

At what separation distance can a proton hover above another proton due to electrostatic repulsion? Hint: Compare gravity to electrostatic repulsion. Please show step by step and explain how you got the numbers. Thanks

It has been proposed that we could explore Mars using inflated balloons to hover just above the surface. The buoyancy of the atmosphere would keep the balloon aloft. The density of the Martian atmosphere is 0.0154 kg/m3 (although this varies with temperature). Suppose we construct these balloons of a thin but tough plastic having a density such that each square meter has a mass of 4.90 g. We inflate them with a very light gas whose mass we can neglect.

Part A

What should be the radius of these balloons so they just hover above the surface of Mars?

Part B

What should be the mass of these balloons so they just hover above the surface of Mars?

Part C

If we released one of the balloons from part A on earth, where the atmospheric density is 1.20 kg/m3, what would be its initial acceleration assuming it was the same size as on Mars?

two skaters collide and embrace, in a completely inelastic collision. boomer, whose mass is 83 kg, is originally moving east with v=6.2km/hr. sooner whose. mass is 55kg, is originally moving north with v=7.8km/hr. (a) what is the velocity of the couple after impact? (b) what is the velocity of the center of mass of two skaters before and aafter collision? (c) what is the fractional change in the Kinect energy of the skaters because of the collision?

An ancient club is found that contains 160 g of pure carbon and has an activity of 6.5 decays per second. Determine its age assuming that in living trees the ratio of ( 14 C 12 C ) atoms is about 1.40 × 10 − 12 . Note that the half life of carbon-14 is 5700 years and the Avogadro number is 6.02 × 10 23.

Answer in years

For what range of object positions does a bi-convex lens of focal length f form a real image?

What is the buoyant force on a helium balloon in air if the balloon is spherical with diameter 18.0 cm ?

A large rock is propelled off the edge of a cliff at an initial velocity of 14 m/s and an angle of 45

A beam of protons is accelerated through a potential difference of 0.720 kV and then enters a uniform magnetic field traveling perpendicular to the field.

A)

What magnitude of field is needed to bend these protons in a circular arc of diameter 1.79 m ?

Express your answer in tesla to three significant figures.

B)

What magnetic field would be needed to produce a path with the same diameter if the particles were electrons having the same speed as the protons?

Express your answer in tesla to three significant figures.

An electric current through hydrogen gas produces several distinct wavelengths of visible light.

a) What are the wavelengths of the hydrogen spectrum if they form first-order maximum at angles of 24.2, 25.7, 29.1 and 41.0 degrees when projected on a diffraction grating having 10,000 lines per cm?

b) What do the minimum and maximum angles become if a 1000 line-per-cm diffraction grating is used? Sketch result.

c) Discuss relationship between further reductions in lines-per-cm and the new angles for the minimum and maximum wavelengths.

d) Why is this important when designing spectroscopic experiments?

Will we someday look back on the 20th century as a time when we used an "ancient form of power transmission called electricity"? Are there better ways to carry power? Fuel pipelines? Lasers? Anything else? How important is power transmission?

On the way to lower floors, an elevator begins its descent from rest at a constant acceleration, ascending the first 0.5 m in 0.85s. What is the apparent weight of a 75 kg man inside the accelerator during this time interval?

.1 kn

.18 kn

.74 kn

.3 kn

Two charges are placed on the x-axis: one is placed at x = 3 m and the other is at x = -3 m. The magnitude of both charges is 5 µC but the blue one (at x = -3 m) is positive while the red one (at x = +3 m) is negative 1.What is the x-component of the electric field at (x, y) = (0 m, +4 m)? 3) Now the positive and negative charge switch places. The magnitude of the charges is still 5 µC where the blue one (now at x = +3 m) is positive and the red one (now at x = -3 m) is negative. What is the x-component of the electric field at (x, y) = (0 m, +4 m)? 4)Now both charges (still at x = -3 m and x = +3 m) are positive. The magnitude of the charges is still 5 µC. What is the y-component of the electric field at (x, y) = (0 m, +4 m)? 5)Finally, both charges (still at x = -3 m and x = +3 m) are negative. The magnitude of the charges is still 5 µC. What is the y-component of the electric field at (x, y) = (0 m, +4 m)?

Birds have evolved to the ability to control their motions through the air by controlling the forces exerted on their bodies by the air; the contact forces on a bird by the air plus the force of gravity on the bird by the Earth determine the change in motion of the bird at any instant of time. In this problem, you will be asked to use what you know about acceleration to track the motion of a diving hawk.

A hawk is flying horizontally Southward at an altitude of 165.0  m and at a speed of 2.10  m/s when he spots a slow-flying finch ahead of his current location and below his current path. At time zero, the hawk starts a dive by controlling the contact forces on him by the air so as to produce an acceleration of 5.30  m/s2 in a direction 69.0  degrees below horizontally Southward for a time of 1.250 seconds.

At the end of the 7.5-s interval, the hawk misses the finch and has to "put on the brakes". He does so by controlling the contact forces on him by the air so as to produce an acceleration of 4.651  m/s2 in a direction 70.104  degrees above horizontally Northward for a time of 1.5 seconds.

1. What is the hawk's final velocity at the end of the 1.5-s interval?

2.

Once again, please assume that the hawk's acceleration during the 1.5-s interval is constant. What is the hawk's displacement during the 1.5-s interval?

Give your answer as an ordered pair, with magnitude first, followed by a comma, then followed by the direction. Give the direction in terms of an angle measured below the horizontally Southward direction.

You have now been tracking the hawk's motion for a total of 1.250 + 7.5 + 1.5 = 10.25 seconds.

3. What is the total Southward displacement of the hawk during those 10.25 seconds? Specify the direction with a plus or minus sign assuming that Southward is positive and Northward is negative.

4. Finally, what is the final altitude of the hawk at the end of those 10.25 seconds?

A coin is moving in a horizontal circle in a cone. The cone has height 70 cm and radius 20 cm. The coin is at a height halfway up. The coefficient of static friction is 0.3. The mass of the coin is 5 g. How fast is the coin moving to stay at this height?If the velocity is halved what will the height of the coin be now?