A uniform spherical shell of mass M = 2.0 kg and radius R = 13.0 cm rotates about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 1.92×10^-3 kg m² and radius r = 4.0 cm, and its attached to a small object of mass m = 4.0 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance h = 1.1 m from rest: Use work - energy considerations.

A uniform stationary ladder of length L = 4.2 m and mass M = 19 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is μ = 0.38. The ladder makes an angle θ = 53° with respect to the floor. A painter of mass 8M stands on the ladder a distance d from its base.

a. Find the magnitude of the normal force N, in newtons, exerted by the floor on the ladder.

b. Find an expression for the magnitude of the normal force NW exerted by the wall on the ladder.

c. What is the largest distance up the ladder dmax, in meters, that the painter can stand without the ladder slipping?

Lecture 4. Interfacial phenomena and membranes

• How are proteins positioning themselves on the surface of membranes?
• What are liposomes, how are they prepared and for what purposes are they used?
• Which factors of phospholipids are important in determining the fluidity of membranes?
• What are the differences between the phospholipids?
• What are the causes of structural bending of the membrane

A 6 (mu Coulomb) point charge is located at the origin and a - 2.5 (mu Coulomb) point charge is located 1m to the right along the X-axis. Determine the point (besides infinity) at which the electric field is 0.

Please show steps and explaination. Thanks in advance!

Two carts with masses 250. g and 200. g are free to slide without friction on a horizontal airtrack.  The 250.g cart is pushed against a spring, compressing it by 3.00 cm, then released.  It slides towards the initially stationary 200 g mass and collides with it.  After the collision the 200. g mass has a forward velocity of 0.450 m/s and the 250. g mass has a forward velocity of 0.250 m/s.
a)  What was the velocity of the 250. g cart just before the collision?
b)  What was the spring constant?

A cue ball traveling at 7.77 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30.0° with its original direction of travel.

(b) Find the speed of each ball after the collision.

A pitched baseball (m=0.3 kg) reaches a catcher’s glove travelling at a velocity of 28 m/s. Calculate the ball’s: A) momentum, B) kinetic energy. How much impulse is required to catch the ball? If the hand moves backward 32cm while the person is catching it, what is the average force applied to the ball? How much time will it take before the ball stops? What is the average power of this contact?

Spaceman Spiff overflies the earth 4 times as you observe him. For each of the velocities below calculate how long and how tall Spaceman Spiffs spaceship will appear to be to you if he measured it as 100 m in length and 10 m in height just before he overflew the earth.

A string or rope will break apart if it is placed under too much tensile stress. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density 7850 kg/m3 and will break if the tensile stress exceeds 7.0×108N/m2. You want to make a guitar string from a mass of 3.5 g of this type of steel. In use, the guitar string must be able to withstand a tension of 900 N without breaking. Your job is the following.

1.Determine the maximum length the string can have.

2.Determine the minimum radius the string can have

3.Determine the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.

An 7.90-cm-diameter, 310 g solid sphere is released from rest at the top of a 1.60-m-long, 17.0 ∘ incline. It rolls, without slipping, to the bottom.

What is the sphere's angular velocity at the bottom of the incline?

What fraction of its kinetic energy is rotational?

1. The spring of a toy gun has a force constant of k = 533 N/m and negligible mass. The spring is compressed the length of the gun barrel, 7.25 cm, and a 0.168-g ball is placed against the compressed spring. A constant frictional force of 5.45-N acts on the ball as it travels through the barrel. The ball leaves the barrel at the moment that it loses contact with the spring. The toy gun is ‘fired’ at a height of 1.33-m above the ground. Ignore air resistance.

1. Show how to determine the speed of the ball as it leaves the barrel when the toy gun is oriented horizontally.

2. Show how to determine the distance that the ball travels horizontally, and its speed of impact.

3. Show how to determine the speed of the ball as it leaves the barrel when the toy gun is oriented vertically.

4. Show how to determine the maximum height attained by the ball, and the speed of its impact when it lands on the ground.

If a roadway is banked (super elevated), a car can round the corner at a higher speed than an unbanked curve. What is the maximum speed a 1200kg car could navigate through an 85m radius turn banked at 16.7° if the maximum value of m_s=0.875?

What is the main advantage of FTIR spectroscopy compared to traditional absorption based spectroscopy, which require dispersive elements. Explain why?

1) What is the highest order dark fringe, m,m, that is found in the diffraction pattern for light that has a wavelength of 621 nm and is incident on a single slit that is 1470 nm?

2) You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equipped with two small headlights that are 0.637 m apart. At what distance, in kilometers, are you marginally able to discern that there are two headlights rather than a single light source? Take the wavelength of the light to be 555 nm and your pupil diameter to be 5.17 mm.

Describe the Physics behind how many traffic lights change when a car rolls up to the intersection. Explain with figure as well