A man pushing a crate of mass m = 92.0 kg at a speed of  v = 0.880 m/s encounters a rough horizontal surface of length ℓ = 0.65 m as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.357 and he exerts a constant horizontal force of 297 N on the crate.

A man pushes a crate labeled m, which moves with a velocity vector v to the right, on a horizontal surface. The horizontal surface is textured from the right edge of the crate to a horizontal distance ℓ from the right edge of the crate.

(a) Find the magnitude and direction of the net force on the crate while it is on the rough surface.

(b) Find the net work done on the crate while it is on the rough surface.
J

(c) Find the speed of the crate when it reaches the end of the rough surface.
m/s

A beam of electrons accelerated by a voltage V hits a target made of atoms of atomic number Z=20 . Suppose the atom ( Z=20) has a spherical and uniform distribution of outer electrons , so that Bohr's model can be used to describe its inner electron. An electron from the accelerated beam hits an atom of the target and ejects the innermost electron of the atom. Assuming that the electron of the beam transferred all its kinetic energy to the atom and neglecting the recoil of the atom itself, find

a) the accelerating voltage

b) A K_β transition ( thats is a 3-->1 transition) occurs to fill the vacancy left behind by the ejected electron and the K_{β line is analyzed by a Bragg spectrometer . The first maximum is observed at 4.9⁰ angle . What is the crystal spacing, d?}

(V) Let A ⊆ R, B ⊆ R, A 6= ∅, B 6= ∅ be two bounded subset of R. Define a set A − B := {a − b : a ∈ A and b ∈ B}. Show that sup(A − B) = sup A − inf B and inf(A − B) = inf A − sup B

A capacitor with capacitance 6.00 × 10−5 is charged by connecting it to a 12.0 V battery. The capacitor is disconnected from the battery and connected across an inductor with L=1.50 H.

1. What is the initial energy stored in the capacitor?

2. What are the angular frequency of the electrical oscillations and the period of the

   oscillations?

3. What is the charge on the capacitor 0.0230 s after the capacitor is connected to the

   inductor? Interpret the sign of your answer.

4. What is the current in the inductor 0.0230 s after the capacitor is connected to the

   inductor? Interpret the sign of your answer.

5. At a time t=0.0230 s after the capacitor is connected to the inductor, how much

   energy is stored in the capacitor and how much is stored in the inductor (make sure to compare your answer to part A)?

A block of mass m= 5.00-kg is moving to the right with a speed of v= 2.00 m/son a horizontal,frictionless surface. The block encounters a relaxed(that is, neither compressed nor extended)spring with spring constant k= 2,000.00 N/m.

a.What is the kinetic energy of the block before hitting the spring?

b.What is the kinetic energy of the block when the spring is at maximum compression?

c.How much energy is stored in the spring at maximum compression?

d.How far does the spring compress at its maximum compression?

e.If the spring converts its stored energy completely into motion of the block, what is the speedof the blockafter release from the spring?

f.(For this part of the problem,the surface is not frictionless) Suppose the speed of the block after release from the spring is 1.5 m/s to the left, how much work (sign and magnitude) was done by non-conservative forces between the time when the initial velocity is 2.00 m/s and the time when the velocity = -1.50 m/s?

A particle moves along a line with velocity function ?(?) = ?^2 − ?, where v is measured in meters per second. a. Find distance traveled by the particle in time interval [0, 6] seconds. b. Find the net displacement. 8. Estimate the area from -1 to 9 under the graph of f(x) = 81 – x^2 using five approximating rectangles and midpoints as sample points.

A) Which of the following sets of quantum numbers are valid (enter V) and which are invalid for the known elements? n = 2, l = 3, m_l = 0, m_s = +½ :

B) write the corresponding orbital notation for n = 6, l = 0?

A bullet of mass 148 g and a speed v impacts on a pendulum of mass 6.18 kg and length 200 cm. The bullet embeds itself in the pendulum bob. The pendulum then travels in a complete and perfect circle.

(a) If the pendulum is suspended by a light, stiff rod, what is the minimum speed of the bullet?


(b) If the pendulum is suspended by a string, what is the minimum speed of the bullet?

Calculate V and Z for methyl chloride at 100 ° C and 55bar for the ideal gas equation, by the equation of virial. Data: R = 83.14 cm 3 bar/molK; viral coefficient B equals -242.5 cm3/mol.

According to the case of Cobbs v. Grant, the court said there was not enough evidence to support a verdict of negligence, yet the original gastrectomy led to multiple hospital stays and two follow-up surgeries. These complications were known risks that can occur even if the surgeon performs the operation flawlessly. If you were the patient and knew about these risks, would you have decide to consent to the first surgery? What factors would you consider?