A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 6.60 N is applied. A 0.400-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (Assume that the direction of the initial displacement is positive. Use the exact values you enter to make later calculations.) (a) What is the force constant of the spring? N/m (b) What are the angular frequency ?, the frequency, and the period of the motion? ? = rad/s f = Hz T = s (c) What is the total energy of the system? J (d) What is the amplitude of the motion? cm (e) What are the maximum velocity and the maximum acceleration of the particle? vmax = m/s amax = m/s2 (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. cm (g) Determine the velocity and acceleration of the particle when t = 0.500 s. (Indicate the direction with the sign of your answer.) v = m/s a = m/s2

m_earth = 5.9742 x 10²⁴ kg
r_earth = 6.3781 x 10⁶ m
m_moon = 7.36 x 10²² kg
r_moon = 1.7374 x 10⁶ m
d_{earth to moon} = 3.844 x 10⁸ m (center to center)
G = 6.67428 x 10^-11 N-m²/kg²

A 1900 kg satellite is orbitting the earth in a circular orbit with an altitude of 1500 km.

1) How much energy does it take just to get it to this altitude? 2.26*10^10 J

2) How much kinetic energy does it have once it has reached this altitude? 4.81*10^10 J

3) What is the ratio of the this change in potential energy to the change in kinetic energy? (i.e. what is (a)/(b)?) 0.47

4) What would this ratio be if the final altitude of the satellite were 4200 km?

5) What would this ratio be if the final altitude of the satellite were 3185 km?

Discuss principles of Fick’s first and second Law and explain it’s pharmaceutical application ?

Discuss heat and mass transfer phenomena involved in freeze, spray and spray freeze drying. Discuss the mechanism behind the role of hygroscopicity in the pharmaceutical product ?

Object A is moving due east, while object B is moving due north. They collide and stick together in a completely inelastic collision. Momentum is conserved. Object A has a mass of mA = 16.4 kg and an initial velocity of = 8.40 m/s, due east. Object B, however, has a mass of mB = 28.2 kg and an initial velocity of = 5.43 m/s, due north. Find the (a) magnitude and (b) direction of the total momentum of the two-object system after the collision.

One object is at rest, and another is moving. The two collide in a one-dimensional, completely inelastic collision. In other words, they stick together after the collision and move off with a common velocity. Momentum is conserved. The speed of the object that is moving initially is 22 m/s. The masses of the two objects are 3.2 and 8.0 kg. Determine the final speed of the two-object system after the collision for the case (a) when the large-mass object is the one moving initially and the case (b) when the small-mass object is the one moving initially.

(a) v_f =  

(b) v_f =  

A spherical bubble rises from the bottom of a lake whose temperature is 6 oC at the bottom and 24 oC at the surface. If the bubble doubles its volume by the time it reaches the surface, how deep is the lake?

object m₁ = 1.50 kg starts at an initial height h_1i = 0.290 m and speed v_1i = 4.00 m/s, swings downward and strikes (in an elastic collision) object m₂ = 4.40 kg which is initially at rest.

Determine the height (in m) to which each ball swings after the collision (ignoring air resistance).

m₁= m

m₂= m

Two parallel plates, each charged equally and oppositely to the other, are separated by 8.9500 cm. A proton is let go from rest at the positive plate's surface and, at the same time, an electron is let go from rest at the negative plate's surface. What is the distance between the negative plate and the point where the proton and the electron go by each other?

Note: unlike most questions, this one will need your answer correct to 5 significant digits. Make sure you enter that many into the box below.

A given copper wire has a resistance of 5.10 ? at 20.0°C while a tungsten wire of the same diameter has a resistance of 4.67 ? at 20.0°C. At what temperature will the two wires have the same resistance?

Explain the role of mass transfer in the crystallization process and freeze drying ?

In two vertexes of an equilateral triangle located charge +q and –2q. Find vector of electric field in the third vertex if length of the side of the triangle is a. Diagram is a MUST.

x-ray Equipment Operation and Quality Assurance

Why does the term "density" not apply to digital? How does the histogram help to determine image brightness?

Consider a high energy photon interacting in tissue. The photon first interacts via pair production before undergoing a Compton Interaction. The positron from pair production undergoes annihilation at the end of its life (no longer in-flight). One annihilation photon undergoes a Compton interaction and scatters at an angle of 100 degrees.

Calculate the kinetic energy of the scattered photon.

A case of canned milk weighing 24 ?bs and is released from rest at the top of a plane metal slide which is 30 feet long and inclined of 45º to the horizontal. The air resistance (in pounds) is numerically equal to 1/3 the velocity (in feet per second) and the coefficient of friction on ice is 0.4:

A. Deduce the Differential Equation that models this movement
b. Calculate the velocity of the block at any time "?"
c. Determine the displacement at any time "?"
d. At what time does the milk can reach the end of the shot?