You go out to the barn and start up the egg collecting machine. Eggs slide down a 30 degree ramp with a coefficient of kinetic friction of 0.2. What is the acceleration of the egg as it moves down the ramp?

If the ramp is two meters long, how fast are the eggs moving when they hit the bottom?

If we assume that the eggs are spherical with a radius of 3 cm, mass 200 grams and roll down the ramp instead of sliding, now recalculate how fast they are moving when they reach the bottom.

Charlie kicks a soccer ball up a small incline. On the way up, ball’s acceleration has magnitude |a| = 0.45 m/s2 and is directed in downhill direction. Charlie kicks the ball at the bottom of the incline and then immediately start to walk up the incline with constant speed. Charlie performs twi different trials. a) In the first trial, Charlie kicks the ball with initial speed v0 = 3.4 m/s. Charlie is 2.3-m behind the ball when the ball is at the highest point. What is the speed vC of Charlie? b) Charlie performs the second trial. He kicks the ball with unknown speed v 0 0 but walks with the same speed vC as in the first trial. Charlie is now 0.8 m behind the ball when the ball is at the highest point. What is the initial speed v 0 0 of the ball at the bottom of the hill? (Hint: You need to set-up a quadratic equation for v 0 0 ).

In the figure, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 3.3 m and then collides with stationary block 2, which has mass m2 = 5m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.2 and comes to a stop in distance d within that region. What is the value of distance d if the collision is (a) elastic and (b) completely inelastic?

Two charged droplets of toner ink behave as two shells of uniform surface charge density. (Toner is an insulating material, not conductive.) The two drops have total charge qi, radiusRi, and centre positionri,i= 1,2. Assuming the drops do not overlap, derive the electric potential, V(r), everywhere inside and outside the spheres. Is the voltage (potential) inside shell 1 constant?

Two parts:

a) An object with an initial mass m_i=7and an initial velocity v_i=6m/s making an angle of 40 degrees with the +x axis has, after a time 4 seconds, final velocity v_f=3making an angle of 0 degrees wrt -x. a) Determine the net force acting on the mass corresponding to F_net=(p_f-p_i)/delta(t), needed to produce that change in momentum. b) Now, assuming there is gravity plus a second, contact force acting on the mass, estimate the magnitude of the second contact force applied to the mass over the time t seconds (using F(contact) + F(gravity) = F(net)) and draw the vectors demonstrating graphical addition.

b) An 6 kg mass, moving at an angle of 40 degrees wrt the +x axis with an initial velocity magnitude |5| collides inelastically with an 8 kg mass, moving at an angle of 50 degrees wrt the +x axis and with an initial velocity magnitude v_{1= 3m/s}. Determine a) the angle that the composite object makes with the axis of your choice, b) the magnitude of the final velocity of the single object, as well as c) the heat generated in the collision.

Pure stoichiometric ZnO is heated to 1400 K in an evacuated chamber of a vapor deposition furnace. What is the partial pressure of Zn and O2 generated by the thermal decomposition of ZnO Information you may find useful AC no at 1400K = -183 kJ/mol

Question 6

a. If the contact angle of a liquid with its container walls is 90° what can we say about the different forces involved and what are those forces? Include a discussion of the meniscus in this case. [3 marks]

b. Explain why the pressure inside a bubble is larger than the pressure surrounding the bubble. [2 marks]
c. At the top of a ski lift a 1 tonne concrete block counterweight is supported by a 10 m long steel cable (of 16 mm diameter when not under stress). You must include the mass of the cable when answering the following questions. The density of steel is 8000 kg m-3, the tensile strength of steel is 5.0 x 108 Pa, the Elastic Modulus of steel is 2.1 x 1011 Pa and Poisson’s ratio for steel is 0.28.
i. What is the safety factor of the system? Comment on your answer. [6 marks]
ii. What is the change in diameter of the cable when supporting the counterweight? [3 marks]
iii. What energy is stored in the cable when supporting the counterweight? [2 marks]
iv. Calculate the Bulk and Shear moduli of steel. [4 marks]

How small an object has to be before it starts to show quantum mechanical affects?

Like if we keep hypothetically breaking down a macroscopic object smaller and smaller, in which size (negative power of metre) does it begin to show quantum mechanical affects? Like it being in 2 places unless we measure it's position.

A car can decelerate at -3.25 m/s2 without skidding when coming to rest on a level road.

What would its deceleration be if the road is inclined at 9.2 ∘ and the car moves uphill? Assume the same static friction coefficient.

Classical Mechanics problem:

See if you can prove the so-called virial theorem. This is a statement that relates the average kinetic energy of a stable system to the potential energy of the system. It applies when the force between two particles of the system has a corresponding potentual energy U of the form U = kr^n, where r is the separation of the particles and n is some real number. So, suppose a mass m moves in a circular orbit about the origin in the field of an attractive central force with potential energy U = kr^n. Show that the kinetic energy T of the particle is T = nU/2.

(Please explain briefly)

A frictionless plane is 10.0 m long and inclined at 28.0°. A sled starts at the bottom with an initial speed of 5.70 m/s up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed v_i. Both sleds reach the bottom of the incline at the same moment.

(a) Determine the distance that the first sled traveled up the incline.

______m

b) Determine the initial speed of the second sled.

_______ m/s

Hi,

For an electron in a cylindrical box, how do we find the Hamiltonian operator?

A satellite is placed in an elongated elliptical (not circular) orbit around the Earth. At the point in its orbit where it is closest to the Earth, it is a distance of 1.00 × 10^6 m from the surface (not the center) of the Earth, and is moving at a velocity of 5.14 km/s. At the point in its orbit when it is furthest from the Earth it is a distance of 2.00×10^6 m from the surface of the Earth. (Note that the Earth has a mass of 5.97×1024 kg and a radius of 6.37×106 m. )

(a) How fast is the satellite moving when it is at its furthest point from the Earth?

(b) If, at the closest approach to the Earth, the satellite could be deflected so that it had the same velocity as before, but was now traveling directly away from the Earth, how far from the surface of the Earth would it get before it stopped, and then started to fall back to the Earth?

Some fusion reactors use an induction process in which thermal neutrons collide with deuterium particles that are essentially twice as massive (consisting of one proton and one neutron). Consider a scenario in which a neutron is traveling at 1500 m/s when it collides elastically with a deuterium particle that is initially at rest. Find the magnitude of the neutron's recoil velocity (in m/s).

An air hockey puck of mass 0.42 kg is traveling at 3.5 m/s in a direction 30^o North of East when it encounters another puck of mass 0.36 kg traveling 40^o North of West at 2.8 m/s. The pucks were recently handled by my children so now they are sticky and collide inelastically. Find the magnitude of their velocity (in m/s) after the collision.

The figure shows a cross section across a long cylindrical conductor of radius a = 2.97 cm carrying uniform current 27.5 A. What is the magnitude of the current's magnetic field at radial distance (a) 0, (b) 2.10 cm, (c) 2.97 cm (wire's surface), (d)3.84 cm?