NAME (PLEASE PRINT)_____________________________ STUDENT #_________________

PHYSICS 025–001 Quiz 4 (60 min.) 21 November 2003 W = ⋅∆F s (const. F) W τ θ= ∆ (const. τ) mgyU gravity = or rGMm− . RGMve 2=

21spring 2U kx= non-consW U K= ∆ + ∆ 21

trans 2K mv= 21rot 2K Iω= vF ⋅== dtdWP or wτ

1. A sled is pulled along a horizontal surface by a rope that makes an angle of 30o to the horizontal. The tension in the rope is 50 N and the sled moves 10 m. The work done by the rope tension in pulling the sled is

A) 125 J B) 250 J C) 288 J → D) 433 J E) 500 J 2. A good example of kinetic energy is provided by: A) a wound-up clock spring B) the raised weights of a grandfather's clock → C) a tornado D) a gallon of gasoline E) an automobile storage battery 3. The total mechanical energy E of an object is conserved if A) frictional forces are present B) the kinetic energy is constant C) the potential energy is constant → D) no work is done by non-conservative forces E) no work is done by conservative forces 4. Three balls are thrown out of a window at the same initial speed. Ball 1 is thrown straight out, 2 is thrown

downward, and 3 is thrown straight up. Just before they hit the ground, their speeds are related by A) 1 2 3v v v> > B) 1 2 3v v v< < → C) 1 2 3v v v= = D) 1 2 3v v v< = E) 1 2 3v v v= < 5. An artificial satellite orbits the Earth in an elliptical orbit. It is always high above the

atmosphere, and so experiences no air resistance. As it gets closer to the Earth, its kinetic energy

→ A) increases B) decreases C) stays constant D) can increase or decrease depending on details of the orbit shape E) is undefined 6. A man pushes a 200-kg crate up a ramp to a point 3.00 m higher than its starting point. It starts and ends at

rest. The man does 8.00 kJ of work in this process. If g = 10 m/s2, the work done by the friction force is A) −1.00 kJ → B) −2.00 kJ C) −6.00 kJ D) −7.40 kJ E) −8.00 kJ 7. A 1200-kg car is accelerated from 10 m/s to 30 m/s. How much work does this require? A) 240 kJ → B) 480 kJ C) 600 kJ D) 960 kJ E) 1200 kJ 8. A 100-W motor is used to

pump water through a vertical height of 20 m. How much water per minute can it supply? Take g = 10 m/s2

For a constant force, 1030cos50cos ×=∆= sFW θ

Kinetic energy is energy of motion. All the other choices different forms of potential energy (elastic, gravitational, chemical)

Since energy is conserved, 0=∆+∆ UK . Since all thre balls fall through the same vertical distance, ∆U is the same for all 3. Thus ∆K must also be the same. Since all 3 have the same initial speed, they must have the same final speed.

When the satellite gets closer to the Earth, i.e. lower, its potential energy decreases. Since total energy is conserved, its kinetic energy must increase.

Since UKWW ∆+∆=+ frictionman ,

( ) 3manfriction 1000.81000.3200 ×−××=−∆= WUW

( ) 02221

net +−=∆+∆= if vvmUKW

The work done by the pump in 1 minute 2060100pump ×=×= mgW . Solve for m.

A) 5 kg B) 10 kg → C) 30 kg D) 100 kg E) 300 kg 9. The motor of a potter’s wheel provides 150 W of power to keep it turning at a constant rate of 2.00 rev/s.

The magnitude of the frictional torque opposing its motion is → A) 11.9 N⋅m B) 75.0 N⋅m C) 150 N⋅m D) 235 N⋅m E) 300 N⋅m 10. Planet X has the same mass as the Earth but four times the radius. If the escape velocity from the Earth is

ve, the escape velocity from planet X is A) ve/4 → B) ve/2 C) ve

D) 2ve

E) 4ve

11. A 2.5-kg block slides head on into a spring with a spring constant of 320 N/m.

When the block stops (momentarily), it has compressed the spring by 7.5 cm.

2 a. Find the change in potential energy of the block-spring system from the time the block hits the spring to the time it stops (momentarily).

2 b. If the coefficient of kinetic friction between the block and the horizontal surface is 0.25, find the work

done by friction on the block from the time it hits the spring to the time it stops. 1 c. Find the kinetic energy of the block just as it hits the spring. 12. An elevator and its contents (white rectangle) have a mass of 2.00×103 kg. It is counterweighted

by a piece of metal of mass 1.80×103 kg, which falls as the elevator rises. A motor (not shown) drives the pulley to raise the elevator.

2 a. Calculate the change in potential energy ∆U of this system when the elevator rises 20.0 m.

1 b. How much energy must the motor provide to move the system through 20.0 m as in part a. at constant speed?

2 c. If the pulley radius is 0.25 m, what is the torque on the pulley provided by the motor? [Hint: Use

W = τ ∆θ ].

2.5 kg 320 N/m

Since the angular speed is constant, τnet = 0. Thus the frictional torque is the same magnitude as the torque provided by the motor. τω=P so

( )πτ 200.2100 ×=

If the mass is constant, rve 1∝ . Thus if r → 4r, ve → ve /2

J 900.00221 =−=∆ fkxU

J 459.0075.08.95.225.0frictionfriction −=×××−=−=∆−= mgxsfW kµ

Since UKW ∆+∆=friction , then J 36.1900.0459.0 −=−−=∆K . Since 0=fK , J 36.1=iK

( ) ( ) J 1092.30.208.91080.100.2 43counterelevator ×=×××−=∆−+∆=∆ ygmygmU

Since UKW ∆+∆=motor , J 1092.3 4motor ×=W

( ) mN 49025.00.201092.3 4motor ⋅=×=∆= θτ W . Here we have used θ∆=∆ rs