Safia

A fireman standing on an 11 m high ladder operates a water hose with a round nozzle of diameter 1.38 inch. The lower end of the hose (11 m below the nozzle) is connected to the pump outlet of diameter 2.6 inch. The gauge pressure of the water at the pump is P (gauge) pump = P (abs) pump − Patm = 52 PSI = 358.527 kPa . Calculate the speed of the water jet emerging from the nozzle. Assume that water is an incompressible liquid of density 1000 kg/m3 and negligible viscosity. The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.

15. A light spring of constant 165 N/m rests vertically on the bottom of a large beaker of water. A 4.1 kg block of wood of density 655 kg/m3 is connected to the top of the spring and the block-spring system is allowed to come to static equilibrium.

Find the density of seawater at a depth where the pressure is 2400 atm if the density at the surface is 1010 kg/m3 . Seawater has a bulk modulus of 2.3 × 109 N/m 2 . Answer in units of kg/m3 .

Find the density of seawater at a depth where

the pressure is 1300 atm if the density at the

surface is 1050 kg/m3

. Seawater has a bulk

modulus of 2.3 × 109 N/m

2

.

Answer in units of kg/m3

A fireman standing on a 9.6 m high ladder operates a water hose with a round nozzle of

diameter 3.29 inch. The lower end of the hose

(9.6 m below the nozzle) is connected to the

pump outlet of diameter 4.63 inches. The gauge

pressure of the water at the pump is

P

(gauge)

pump = P

(abs)

pump − Patm

= 52.7 PSI = 363.354 kPa .

Calculate the speed of the water jet emerging from the nozzle. Assume that water is an

incompressible liquid of density 1000 kg/m3

and negligible viscosity. The acceleration of

gravity is 9.8 m/s

2

.

Answer in units of m/s.

A horizontal pipe of diameter 1.1 m has a

smooth constriction to a section of diameter

0.66 m. The density of oil flowing in the pipe

is 821 kg/m3 .

If the pressure in the pipe is 8200 N/m2

and in the constricted section is 6150 N/m2 ,

what is the rate at which oil is flowing?

Answer in units of m3/s.

Find the density of seawater at a depth where the pressure is 1300 atm if the density at the surface is 1050 kg/m3. Seawater has a bulk

modulus of 2.3 × 109 N/m2.

Answer in units of kg/m3

A merry-go-round rotates at the rate of

0.37 rev/s with an 88 kg man standing at

a point 1 m from the axis of rotation.

What is the new angular speed when the

man walks to a point 0 m from the center?

Consider the merry-go-round is a solid 28 kg

cylinder of radius of 1 m.

Answer in units of rad/s.

What is the change in kinetic energy due to

this movement?

Answer in units of J.

a) An amusement park ride consists of a rotating circular platform 9.06 m in diameter from which 10 kg seats are suspended at the end of 1.08 m massless chains. When the system rotates, the chains make an angle of 26.9◦ with

the vertical.

The acceleration of gravity is 9.8 m/s2.

What is the speed of each seat?

Answer in units of m/s.

b) If a child of mass 51 kg sits in a seat, what is

the tension in the chain (for the same angle)?

Answer in units of N.

The tape in a videotape cassette has a total

length 240 m and can play for 2 h. As the tape

starts to play, the full reel has an outer radius

of 38 mm and an inner radius of 13 mm. At

some point during the play, both reels will

have the same angular speed.

What is this common angular speed?

Answer in units of rad/s.

You weigh 800 N.

What would you weigh if the Earth were

four times as massive as it is and its radius

were six times its present value?

Answer in units of N

A jet aircraft is traveling at 272 m/s in horizontal flight. The engine takes in air at a

rate of 91.8 kg/s and burns fuel at a rate of

4.01 kg/s. The exhaust gases are ejected at

552 m/s relative to the aircraft.

Find the thrust of the jet engine.

Answer in units of N.

Find the delivered power.

Answer in units of W.

A massless spring with force constant

320 N/m is fastened at its left end to a vertical

wall, as shown below.

The acceleration of gravity is 9.8 m/s2.

Initially, the 7 kg block and 2 kg block rest

on a horizontal surface with the 7 kg block in

contact with the spring (but not compressing

it) and with the 2 kg block in contact with the

7 kg block. The 7 kg block is then moved to

the left, compressing the spring a distance of

0.6 m, and held in place while the 2 kg block

remains at rest as shown below.

Determine the elastic energy U stored in

the compressed spring.

Answer in units of J.

The 7 kg block is then released and accelerates

to the right, toward the 2 kg block. The

surface is rough and the coefficient of friction

between each block and the surface is 0.5. The

two blocks collide, stick together, and move

to the right. Remember that the spring is not

attached to the 7 kg block.

Find the speed of the 7 kg block just before

it collides with the 2 kg block.

Answer in units of m/s.

Find the final speed of both blocks (stuck

together) just after they collide.

Answer in units of m/s.

Find the horizontal distance the blocks move

before coming to rest.

Answer in units of m.

A crate is pulled by a force (parallel to the

incline) up a rough incline. The crate has an initial speed shown in the figure below. The crate is pulled a distance of 6.03 m on the

incline by a 150 N force.

The acceleration of gravity is 9.8 m/s2.

a) What is the change in kinetic energy of

the crate?

Answer in units of J.

b) What is the speed of the crate after it is

pulled the 6.03 m?

Answer in units of m/s.

Assume that the North American continent

can be represented by a slab of rock 5200 km

on a side and 35 km deep and that the rock

has an average mass density of 2700 kg/m3.

The continent is moving at the rate of about

3.8 cm/year.

What is the mass of the continent?

Answer in units of kg.

What is the kinetic energy of the continent?

Answer in units of J.

A jogger (of mass 64 kg) has the same kinetic

energy as that of the continent.

What would his speed be?

Answer in units of m/s