Master the Art of Physics: Comprehensive Examples and Expert Advice

A constant potential difference of 12V is maintained between the terminals of a 0.25 micro-F parallel plate air capacitor. 
A. A sheet of Mylar is inserted between the plates of the capacitor completely filling the space between the plates. When this is done how much additional charge flows into the positive plate of the capacitor? (K for mylar = 3.1) 
B. What is the total induced charge on either face of the mylar sheet? 
C. What effect does the mylar sheet have on the electric field between the plates? Explain how you can reconcile thiswith the increase of charge on the plates, which acts to increase the electric field.

In a truck-loading station at a post office, a small 0.200-kg package is released from rest a point A on a track that is one quarter of a circle with radius 1.60 m.The size of the packageis much less than 1.60m, so the package can be treated at aparticle. It slides down the track and reaches point B with a speed of 4.80 m/s. From point B, it slides on a level surface a distanceof 3.00 m to point C, where is comes to rest. 
(a) What is the coefficient of kinetic friction on the horizontal surface? 
(b) How much work is done on the package by friction as it slides down the circular arc from A to B?

A golfer hits a golf ball at an angle of 25 degrees to the ground. If the golf ball covers a horizontal distance of 301. 5 m, what is the ball's maximum height? (Hint: at the top of its flight, the ball's vertical velocity component will be zero.)

A block is on a frictionless table, on earth. The block accelerates at ${\displaystyle 5.3\frac{m}{s^2}}$ when a 10 N horizontal force is applied to it. The block and table are set up on the moon. The acceleration due to gravity at the surface of the moon is ${\displaystyle 1.62\frac{m}{s^2}}$. A horizontal force of 5N is applied to the block when it is on the moon. The acceleration imparted to the block is closest to: 
a) ${\displaystyle 2.9\frac{m}{s^2}}$ 
b) ${\displaystyle 3.2\frac{m}{s^2}}$ 
c) ${\displaystyle 3.4\frac{m}{s^2}}$ 
d) ${\displaystyle 2.7\frac{m}{s^2}}$ 
e) ${\displaystyle 2.4\frac{m}{s^2}}$

At a waterpark, sleds with riders are sent along a slippery, horizontal surface by the release of a large, compresesed spring. The spring with a force constant k= 4000N/m and negligible mass rests on the frictionless horizontal surface. One end is incontact witha stationary wall. A sled and rider with total mass 70.0kg are pushed against the other end, compressing the spring 0.375m. The sled is then released with zero initial velocity. What is the sled's speed when the spring a) returns to its uncompressed length? b) is still compressed 0.200m?

A race driver has made a pit stop to refuel. Afterrefueling, he leaves the pit area with an acceleration whosemagnitude is ${\displaystyle 6.0\frac{m}{s^2}}$ ; after 4.0s he enters the mainspeedway. At the same instant, another car on thespeedway and traveling at a constant speed of 70.0m/sovertakes and passes the entering car. If the entering carmaintains it acceleration, how much time is required for it tocatch the other car? 
I tried to find the V for the car in the pit area. Isthat the right first step; what do I do next? Any help would begreat.

Two astronauts, one mass 60 Kg and the other 80 Kg, areinitially at rest in outer space. They then push each otherapart. How far apart are they when the lighter astronaut hasmoved 12 m. Is it -12m? velocities should be the samein free fall.

A radar station, located at the origin of xz plane, as shown in the figure , detects an airplane coming straight at the station from the east. At first observation (point A), the position of the airplane relative to the origin is $\overrightarrow{R_A}$. The position vector $\overrightarrow{R_A}$ has a magnitude of ${\displaystyle {360}^m}$ and is located at exactly ${\displaystyle {40}^{\circ }}$ above the horizon. The airplane is tracked for another ${\displaystyle {123}^{\circ }}$} in the vertical east-west plane for ${\displaystyle {5.0}^s}$, until it has passed directly over the station and reached point B. The position of point B relative to the origin is $\overrightarrow{R_B}$ (the magnitude of $\overrightarrow{R_B}$ is ${\displaystyle {880}^m}$). The contact points are shown in the diagram, where the x axis represents the ground and the positive z direction is upward.

Define the displacement of the airplane while the radar was tracking it: ${\overrightarrow{R}}_{BA}={\overrightarrow{R}}_B-{\overrightarrow{R}}_A$. What are the components of ${\overrightarrow{R}}_{BA}$
Express ${\overrightarrow{R}}_{BA}$ in meters as an ordered pair, separating the x and z components with a comma, to two significant figures.

The magnetic field ${\displaystyle \overrightarrow{B}}$ in acertain region is 0.128 ,and its direction is that of the z-axis in the figure.

Part A
What is the magnetic flux across the surface abcd in the figure?
Part B
What is the magnetic flux across the surface befc ?
Part C What is the magnetic flux across the surface aefd?
Part D
What is the net flux through all five surfaces that enclose the shaded volume?

A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2 kg physics textbook horizontally toward the north shore , at a speed of 5.0 m/s. How long does ittake him to reach the south shore?

A 500 g ball swings in a vertical circle at the end of a1.5-m-long string. When the ball is at the bottom of the circle,the tension in the string is 15 N. 
What is the speed of the ball at that point?

The tires of a car make 65 revolutions as the car reduces its speed uniformly from 100 km/h to 50 km/h. The tires have diameter of 0.80 m. a) What was the angular acceleration? b)If the car continues to decelerate at this rate, how much more timeis required for it to stop?
For part a, I thought my method was pretty legitimate, but myanswer didn't match the one in the back of the book. The backof the book had the answer -4.4 ${\displaystyle ra\frac{d}{s^2}}$, whereas Igot $-1.59\cdot {10}^4$ ${\displaystyle ra\frac{d}{s^2}}$

A marble moves along the x-axis. The potential-energy functionis shown in Fig. 1
a) At which of the labeled x-coordinates is the force on the marble zero?
b) Which of the labeled x-coordinates is a position of stable equilibrium?
c) Which of the labeled x-coordinates is a position of unstable equilibrium?

A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 220 mph at an altitude of 800 m. The positive x and y directions are defined. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shownin the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g=9.80 .

A space traveler weights 540 N on earth. what will the traveler weigh on another planet whose radius is three times that of earth and whose mass is twice that of earth ?

A car is initially going 50 ft/sec brakes at a constant rate (constant negative acceleration), coming to a stop in 5 seconds.
a) graph the velocity from $t=0$ to $t=5$
b) how far does the car travel?
c) how far does the car travel if its initial velocity isdoubled, but it brakes at the same constant rate?

A swimmer is capable of swimming 0.45m/s in still water (a) If sheaim her body directly across a 75 m wide river whose current is0.40m/s how far downstream ( from a point opposite her startingpoint ) will she land ? (b) how long will it take her to reach theother side

A loud speaker of mass 19.0 kg is suspended a distance of 1.00 m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of 3.30 m.
A) What is the tension in each ofthe cables? (Use ${\displaystyle 9.80\frac{m}{s^2}}$ for the magnitude of the acceleration due to gravity.)

Two blocks with masses 4.00 kg and 8.00 kg are connected by string and slide down a 30.0 degree inclined plane. The coefficient of kinetic friction between the 4.00-kg block and the plane is 0.25; that between the 8.00-kg block and the plane is 0.35.
a) Calculate the acceleration of each block
b) Calculate the tension in the string
c) What happens if the positions of the block are reversed, so that the 4.00-kg block is above the 8.00-kg block?

An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 m/s. If the alha particle has a mass of 4.0u and the original nucleus has a mass of 222u. What speed does the alpha particle have when it is emitted?