Master the Art of Physics: Comprehensive Examples and Expert Advice

You are on the roof of the physics building, 46.0 m above the ground. Your physics professor, who is 1.80 tall, is walking along side the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your professor's head, how far from the building should the professor be when you release the egg? Assume that the egg is in free fall.Take the free fall acceleration to be ${\displaystyle 9.80\frac{m}{s^2}}$

A block of mass m=2.20 kg slides down a 30 degree incline which is 3.60 m high. At the bottom, it strikes a block of mass=7.00 kg which is at rest on a horizontal surface in the picture. If the collision is elastic, and friction can be ignored, determine (a)the speeds of the two blocks after the collision, and (b) how far back up the incline the smaller mass will go.

Two point charges ${\displaystyle q_1=+2.40}$ nC and ${\displaystyle q_2=-6.50}$ nC are 0.100 m apart. Point A is midway between them and point B is 0.080 m from ${\displaystyle q1}$ and 0.060 m from ${\displaystyle q_2}$. Take the electric potential to be zero at infinity.

(a) Find the potential at point A.
(b) Find the potential at point B.
(c) Find the work done by the electric field on a charge of 2.50 nC that travels from point B to point A.

Answer the following T/F questions based on the behavior of the circuit in the above Figure 5:
(1) A transient current flows for a short time after the RELAY is switched to either the N.O.("normally open") or N.C. ("normally closed") position.
(2)The transient currents that flow in this experiment decays exponentially to zero.
(3)The capacitor charge Q exponentially decays to zero when the RELAY is thrown to position N.O.
(4)When the current I is positive, the capacitor charge Q is decreasing.
(5)When the current I is positive, the measured VOLTAGE IN 2 will be negative.
(6)When the capacitor charge Q is positive, the measured VOLTAGE IN 1 is positive.
(7)The quantity t1/2=? ln 2 is called the half-life of an exponential decay, where ?=RC is the time constant in an RC circuit. The current in a discharging RC circuit drops by half whenever t increases by ${\displaystyle t_{\frac{1}{2}}}$. For a circuit with R=2 k? and C=3 ?F, if the current is 6 am at t=5 ms, at what time (in ms) will the current be 3 mA?

A model airplane of mass 0.750 kg flies in a horizontal circle at the end of a 60.0 m control wire, with a speed of 35.0 m/s. Compute the tension in the wire if it makes a constant angle of 20.0° with the horizontal. The forces exerted on the airplane are the pull of the control wire, the gravitational force, and aerodynamic lift, which acts at 20.0° inward from the vertical.

An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of ${\displaystyle 6.64\cdot {10}^{-27}}$ kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.10 T magnetic field. 
A) What is the diameter of the path followed by this alpha particle? 
B) What effect does the magnetic field have on the speed of the particle? 
C) What are the magnitude of the acceleration of the alpha particle while it is in the magnetic field? 
D) What are the direction of the acceleration of the alpha particle while it is in the magnetic field?

A person who starting from rest at the top of a cliff swings down at the end of a rope,releases it, and falls into the water below. There are two paths bywhich the person can enter the water. Suppose he enters the waterat a speed of 13 m/s via path 1. How fast is he moving on path 2 when he releases the rope at a height of 5.20 m above the water? Ignore the effects of air resistance.

A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?

A stream of water strikes a stationary turbine bladehorizontally, as the drawing illustrates. The incident water streamhas a velocity of +18.0 m/s, while the exiting water stream has avelocity of -18.0 m/s. The mass of water per second that strikesthe blade is 17.0 kg/s. Find themagnitude of the average force exerted on the water by theblade.

If the coefficient of static friction between your coffeecup and the horizontal dashboard of your car is, how fast can you drive on a horizontal roadwayaround a right turn radius of 30.0 m before the cup starts toslide? If you go too fast, in what direction will the cupslide relative to the dashboard?

The spring in the figure (a) is compressed by length delta x . It launches the block across a frictionless surface with speed v0. The two springs in the figure (b) are identical to the spring of the figure (a). They are compressed by the same length delta x and used to launch the same block. What is the block's speed now?

A 5.00 kg package slides 1.50 m down a long ramp that is inclined at ${\displaystyle {12.0}^{\circ }}$ below the horizontal. The coefficient of kinetic friction between the package and the ramp is k =0.310. Calculate 
(a) the work done on the package by friction (b) the workdone on the package by gravity (c) the work done on the package bythe normal force (d) the total work done on the package (e) Ifthe package has a speed of 2.20 m/s at the top of the ramp, what isits speed after sliding 1.50 m down the ramp?

A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force acting at 20.0 degree angle above the horizontal. The block is displaced 5.0 m, and the coefficient of kinetic friction is 0.3. Find the work done on the block by ; a) the 70.0 N force,b) the normal force, and c) the gravitational force. d) what is the increase in the internal energy of the block-surface system due to friction? e) find the total change in the kinetic energy of the block.

The end of the cutting cord on a gas-powered weed cutter is0.15 m in length. If the motor rotates at the rate of 20rev/s, what is the tangential sped of the end of the cord? 
a) 628 m/s 
b) 25 m/s 
c) 19 m/s 
d) 63 m/s 
e) 75 m/s

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)

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Fig. 1) The rope will break if the tension in it exceeds $4.50\cdot {10}^4$N and our hero's mass is 86.5 kg.

 Figure 1 a) If the angle $\theta$ is ${13.0}^{\circ }$, find the tension iin the rope.

b) What is the smallest value the angle $\theta$ can have if the rope is not to break?

An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a constant torque of ${\displaystyle 1950N\cdot m}$ to the propeller, which starts from rest.
a) What is the angular acceleration of the propeller? Model the propeller as a slender rod.
b) What is the propeller's angular speed after making 5.00 revolutions?
c) How much work is done by the engine during the first 5.00 revolutions?
e) What is the instantaneous power output of the motor at the instant that the propeller has turne through 5.00 revolutions?

The rotor (flywheel) of a toy gyroscope hasmass 0.140 kg. Its moment of inertia about its axis is . The mass of the frame is 0.0250 kg. The gyroscopeis supported on a single pivot javascript:void(0); with its center of mass a horizontaldistance of 4.00 cm from the pivot. The gyroscope is precessing ina horizontal plane at the rate of one revolution in 2.20 s. Find the upward force exerted by thepivot. Find the angular speed with which the rotoris spinning about its axis, expressed in rev/min. Comments

 
Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces ${\displaystyle F_A}$ and ${\displaystyle F_B}$ exerted on the unit by the horizontal cables is parallel to the line L, and ${\displaystyle F_A=4200}$ N. Determine ${\displaystyle F_B}$? Determine the magnitude of ${\displaystyle F_A+F_B}$?

(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?