Solve the wave equation using The Laplace Transformation . ( in detail please )

Boxing gloves are padded to lessen the force of a blow.

(a) Calculate the force exerted by a boxing glove on an opponent's face, if the glove and face compress 7.00 cm during a blow in which the 8.00 kg arm and glove are brought to rest from an initial speed of 10.0 m/s.
N
(b) Calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and face would compress only 2.00 cm. (Assume the total mass of the arm remains 8.00 kg.)
N
(c) Discuss the magnitude of the force with glove on. Does it seem high enough to cause damage even though it is lower than the force with no glove?

In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 70.0 m along a 25° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.)

(a) starting from rest
final speed
m/s
time taken
s

(b) starting with an initial speed of 3.00 m/s
final speed
m/s
time taken
s

(a) How high a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 76.0 km/h?
m
(b) If, in actuality, a 750 kg car with an initial speed of 76.0 km/h is observed to coast up a hill to a height 11.0 m above its starting point, how much thermal energy was generated by friction?
J
(c) What is the average force of friction if the hill has a slope 2.5° above the horizontal? (Explicitly show on paper how you follow the steps in the Problem-Solving Strategy for energy found on pages 159 and 160. Your instructor may ask you to turn in this work.)
N (down the slope)

When a golf ball or basketball is dropped to the pavement, it bounces backup. (i) Is a force needed to make it bounce back up? (ii) if so, what exerts the force?

(b) Whiplash sometimes results from an automobile accident when the victim

Explain your interpretation and understanding of The Doppler Effect.

Along with that I also would like you all to discuss the interesting facts about light

A number 14 copper wire has a diameter of 1.628 mm. Calculate the resistance of a 34.0 m long piece of such wire.
(Use 1.72×10^-8 Ωm for the resistivity of copper.)

2.809×10^-1 Ohm
For safety, the National Electrical Code limits the allowable amount of current which such a wire may carry. When used in indoor wiring, the limit is 15.0 A for rubber insulated wire of that size. How much power would be dissipated in the wire of the above problem when carrying the maximum allowable current?

6.321×10¹ W

What would be the voltage between the ends of the wire in the above problem?

4.214 V

What is the current density in the wire when it is carrying the maximum allowable current? (Current density is the current in the wire divided by the cross sectional area of the wire.)

NEED HELP
What is the drift velocity of the electrons when the wire is carrying the maximum allowable current?
(The density of electrons in copper is 8.47×10²⁸ m^-3.)

NEED help

A cylinder radius R is rolling down a slope, angle ø. There is sufficient friction that the cylinder rolls without slipping, but do not assume the friction is maximum static friction. Known quantities are R, g, ø

What is the linear acceleration of the cylinder down the slope?

Normal forces are applied uniformly over the surface of a spherical volume of water whose radius is 20.0 cm. If the pressure on the surface is increased by 200 MPa, by how much does the radius of the sphere decrease?

Three blocks of mass ?1=?2=?3=1?? are stacked on a table as shown. The surfaces of the blocks and table are coated with Teflon and all have the same small coefficient of friction, ??=??=0.01. A force of 30N is applied straight down on the top mass as shown.

a) Draw a free body diagram for each mass labelling all forces.

b) Which direction might the bottom mass move and why?

c) What is the acceleration of the top mass?

A 4.00 kg ball traveling North with a momentum of 11.2 kg.m/s collides with a 6.0 kg ball traveling West with a momentum of 18 kg.m/s. The two balls stick together and head off as one. What is the momentum of the combined masses? What is the velocity of the combined masses?

s] From a distance of ra = 8.000 m, a trumpet player plays an A note, f1 = 440.0 Hz, with a sound intensity level of β1 = 58.00 dB. A tuba plays in unison with the trumpet, but is slightly out of tune and has f2 = 437.00 Hz, and its sound intensity level is β2 = 63.50 dB. a) Calculate I1 and I2, the intensities of each instrument separately. b) When they play in unison, how many decibels does their combined sound create? c) What beat frequency is heard? d) If the distance to the instruments is increased to rb = 24.00 m, what are the sound intensity levels (in dB) of the trumpet by itself, the tuba by itself, and the combined instruments?

Question text

Consider a long solenoid of length = 1m, radius = 3.0 cm and 800 turns/m. If the rate of change of current is 40 A/s what voltage is induced?

Select one:

a. 11 mV

b. 0.6 mV

c. 91 mV

d. 70 mV

e. 0.4 mV

You are advised not to open the radiator cap of the radiator of your car(pressure cap) when it is very hot. The reason is that the pressure inside radiator is more than outside atmospheric pressure and hot water will gush out if the cap is opened. Explain why radiators are designed to work under such higher pressure. That is, What is the benefit gained?

A scientist looking for meteorites on Antarctica

finds an irregularly shaped rock and

he wants to determine its density. He determines that the rock’s mass in air is 50

kg.

The Young’s modulus of steel is 200

·

10

9

Nm

-

2

. The ultimate strength of steel is

500

·

10

6

Nm

-

2

.

Q 4(a)

[5

Marks]

He hangs the rock from a

2

-

metre

-

long

steel cable with a diameter of 1

cm. Calculate

the strain and change in length of the cable

.

Q 4(b)

[5 Marks]

What would happen if he had used a cable with a diameter of only 2mm? Explain

your answer.

Thescientist now submerges the rock in a tub of water. He now determines the effective weight to be 38.5kg.

Q 4(c)

[5

Marks]

Calculate the volume and density of the rock

.

Q 4(d)

[5 Marks]

If the scientist had used alcohol (ρ=789kg/m3), would he have found a larger or smaller effective weight when the rock is submerged?

Explain your answer.

draw hertzsprug russell diagram for an open star cluster and a globular cluster and discuss the differences