Boost Your Understanding of Magnetism Physics with Plainmath

Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height of 13 m into 35 cm. of water. Assuming that he stops just as he reaches the bottom of the water and estimating his mass to be 72 kg, find the magnitudes of the impulse on him from the water.

A 10.0 g marble slides to the left with a velocity ofmagnitude 0.300 m/s on thefrictionless, horizontal surface of an icy, New York sidewalk andhas a head-on elastic collision with a larger 25.0 g marble sliding to the right with a velocityof magnitude 0.150 m/s (Fig. 8.35). 
(a) Find the velocity of each marble (magnitude anddirection) after the collision. (Since the collision is head-on,all the motion is along a line. Take right as the positivex direction.) 
m/s (smaller marble) 
m/s (larger marble) 
(b) Calculate the change in momentum (that is, the momentum afterthe collision minus the momentum before the collision) for eachmarble. 
kgm/s (smallermarble) 
kgm/s (largermarble) 
(c) Calculate the change in kinetic energy (that is, the kineticenergy after the collision minus the kinetic energy before thecollision) for each marble. 
J (smaller marble) 
J (larger marble)

(a) How far from a 50.0-mm-focal-length lens must an object be placed if its image is to be magnified 2.00 X and be real? 
(b) What if the image is to be virtual and magnified 2.00 X?

Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a 1.50 kg ball swings downward and strikes a 4.60kg ballthat is at rest, as the drawing shows. a. using the principle of conservation of mechanicalenergy,find the speed of the 1.50 kg ball just before impact b. assuming that the collision is elastic, find the velocities( magnitude and direction ) of both balls just after thecollision c. how high does each abll swing after the collision, ignoringair resistance?

An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h. After flying for 0.500 h, she find sherself over a town 120 km west and 20 km south of her starting point. a) Find the wind velocity (magnitude and direction). b) If the wind velocity of 40 km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 220 km/h. 
The answers are: 
a) 44.7 km/h, 26.6 deg. west of south 
b) 10.5 deg. north of west

A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge,of positive charge q. 
A) What is the total surface charge q on the interior surface of the conductor (i.s., on the wall of the cavity)? 
C) What is the magnitude ${\displaystyle E_{\int }}$ of the electric field inside the cavity as a function of the distance from the point charge? Let k, as usual, denote ${\displaystyle \frac{1}{4\pi {ϵ}_0}}$. 
D)Will the total charge on the surface of the cavity change? 
Will the totaly charge on the exterior of the conductor change? 
Will the charge on the electric field with in the cavity change? 
Will the charge on the electric field outside the cavity change?

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?

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 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.

A conducting sphere of radius 0.01m has a charge of ${\displaystyle 1.0\times {10}^{-9}C}$ deposited on it. The magnitude of the electric field in N/C justoutside the surface of the sphere is: 
a. 0 
b. 450 
c. 900 
d. 4500 
e. 90000