O Revision Mechanics

7/29/2019 O Revision Mechanics

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Police Car

Car

O LEVEL PHYSICS REVISION

Mechanics

1 A small pebble released from the top of a deep well took 3.0 s to hit the surface of water in the well.

Assume that air resistance is negligible,

(a) write the magnitude of acceleration of the pebble and explain how you arrived at the answer.

(b) sketch the speed-time graph of the pebble. Clearly label the speed and time at which the

pebble hits the surface of the water.(c) calculate the distance travelled by the pebble from the point of release until it hits the surface

of the water in the well.

(d) sketch a distance-time graph of the motion of the pebble. Clearly label the distance and time

at the start and end of the motion.

2 A model rocket is launched from rest. Its engine delivers a constant acceleration of 8.2 m/s2

for a

full 5.0 s, after which the fuel is used up. Assuming that the rocket was launched vertically and thatair resistance is not significant,

(a) sketch a velocity-time graph to show the variation of velocity to time of the rocket motion

from launch until it returns to Earth.

(b) find the maximum altitude reached by the rocket.

(c) find the total time the rocket is in flight.

3 A crane moves from the ground floor to the top of

a building and then descends from the top of the

building. The velocity-time graph of the crane is as

shown.

(a) Find the time taken for the crane to movefrom the ground floor to the top of the

building.

(b) What is the height of the building?(c) Sketch the corresponding acceleration-time

graph for the motion of the crane.

4 A car is travelling along Kranji Expressway at a very high

speed and passes a parked police car. The police car

accelerates immediately and gives signal to the car to stop.

When will the police car meet the car. Express your answer

in seconds.

5 Two cars A and Bare lined up along the traffic junction waiting for the lights to turn green. As the

traffic light turns green, both cars start to accelerate constantly. However the reaction times of thedrivers in both cars A and Bare 0.3 s and 0.8 s respectively. 5.3 s after the lights turned green, the

velocity of carA is 15.0 m/s. It took carB73.5 m to catch up with A.

10 20 30 40 50 60 70

8.0

0

-8.0

v/m/s

t/s


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(a) How long after the lights turn green did carBcatch up with A?

(b) What are the final velocities of carA and B?

(c) Calculate the acceleration of carB.

(d) Sketch the velocity-time graph for both cars. Label cars A and B. Your graph should start from

the time light turns green till the time Bovertakes A.

6 A man shoots a ball vertically upwards at an initial speed of 50 m/s. What is the distance travelled

by the ball 7.0 s after the shoot?

7 A student placed a trolley on a runway. A length of paper tape was attached to the trolley and this

tape passed through a ticker-timer that operates at a frequency of 20 dots per second. The student

then tilted the runway to an angle at which the trolley accelerated when released from the top. The

diagram shows the tape produced as the trolley ran down the slope. The tape has been divided into

three sections, each section containing 5 spaces between adjacent dots.

(a) Which section of the tape was closest to the trolley, and how does the tape indicate that thetrolley accelerated as it ran down the runway?

(b) The student calculated that the average velocity of the trolley during section 1was 80 cm/s.

Show how this result was calculated.(c) What was the average velocity of the

trolley during section 3?

(d) Define acceleration.

(e) Calculate the acceleration of the

trolley.

8 In an army war exercise, a 50 kg crate of ammunition was dropped from high altitude. The

parachutes are deployed 20.0 s after the crate is released. The graph shows the velocity-time pattern

of the motion of the crate. The crate touched down 35.0 s after its release.(a) Describe the motion of the crate from 0 to35 s.

(b) Explain how the net force acting of the cratechanges from 0 to 20 s.

(c) State the net force acting of the crate from15 s to 20 s.

(d) From the graph, state the speed of the cratejust before it lands.

(e) Calculate the impact force on the crate uponlanding if it sinks 2 cm into the ground.

9 On an aircraft carrier, an airplane launcher is effectively a large spring that pushes the plane from

rest for the first 6.0 m of the runway. The planes jet engines supply a constant thrust of 54 000 N

for the entire length of the runway. To take off safely, the 2 000 kg plane needs to have a velocity

of 45 m/s by the end of the runway.

(a) For the first 6.0 m of the journey, what is the effective force on the plane if its acceleration is

108 m/s2?

(b) What is the force that must be provided by the spring, assuming it remains constant?

(c) What is the velocity of the plane at the end of the first 6.0 m of the runway?

(d) For the rest of the runway, the net force that is due to the jet engines is 54 000 N. What is theminimum length of the runway if the plane is to attain a velocity of 45 m/s just before taking

off?

20 cm 40 cm 70 cm


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10 A car of mass 2 000 kg moves along a straight, level road. The engine enables a forward force of

6 000 N to act on the car. An opposing force, comprising air resistance and frictional forces, of

4 000 N also act against the car.

(a) Draw a free body force diagram showing all the forces acting on it.(b) Calculate the acceleration of the car.(c) As the car goes faster with the same forward force, it undergoes decreasing acceleration.

Explain why this happens.

11 A lift, held by a cable, has a mass of 400 kg. Calculate the tension in the cable when it is

(a) stationary(b) moving upwards at a constant speed of 3.0 m/s(c) moving downwards at a constant speed of 1.0 m/s(d) moving upwards at a constant acceleration of 2.0 m/s2(e) moving upwards at a constant deceleration of 4.0 m/s2(f) moving downwards at a constant acceleration of 1.0 m/s2(g) moving downwards at a constant deceleration of 2.0 m/s2

12 A, Band Care three identical blocks resting on a smooth surface. A force of 60 N is applied at oneend as shown. What are the tensions T1, between blocks A and B, and T2, between blocks Band C

in the strings?

13 There are two kinds of quantities in physics, scalarsand vectors.(a) What is the difference between a vector quantity and a scalar quantity?(b) Give one example of a vector quantity and one example of a scalar quantity.(c) A student X, starting at a point P, walks due North for 1.0 h at a constant speed of 4.0 km/h

and then, at the same constant speed, walks 4.0 km due East, finishing at a point Q. In thesame total time but a different constant speed, a second student Ywalks directly from Pto Q.

(i) Calculate the total distance walked by student X;(ii) Determine by drawing a vector diagram,

1 the distance walked by student Y2 the velocity of student Y.

14 Two forces are combined and cause a resultant force.

(a) State the one factor that affects the magnitude of the resultant force?

(b) State the range of the magnitude of the resultant when forces of magnitude 3 N and 4 N arecombined.

15 An experiment is conducted to illustrate the addition of

forces on a stationary object, by using the setup shown. The

two spring balances are attached to the ceiling and an

object of mass 5 kg is hung between the spring balances.

ABand BCare of equal length.

(a) (i) By means of a scale diagram, find the readingon each spring balance when is 30.

(ii) State qualitatively how your answer in (a)(i)would differ if is increased to 60.

(iii) Explain why it is not possible for the weight to be in equilibrium when is 90.

60 NCBAT1 T2


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(b) The experiment is conducted in a lift which is accelerating downwards at 2.0 m/s2.(i) Calculate the magnitude and direction of the resultant force on the object.(ii) Explain whether you would expect the readings on each spring balance to be larger or

smaller than your answer in (a)(i), if is also 30.

16 A boat wants to move from point A to B across the

Singapore River. The current is moving from the left to the

right at a speed of 1.0 m/s. In which direction should theboatman point the nose of his boat if the speed of the boat

in still water is 3.0 m/s? Draw a scale diagram to solve the

problem.

17 A 10 kg mass is suspended by two strings as shown. Using a

scaled vector diagram, find the tensions in the two strings.

18 A wind blowing due East gives a sailing boat a speed of 6.0 m/s. If the tide gives the boat a speed

of 3.0 m/s in the North-East direction, find by scale drawing, the resultant magnitude and direction

of the velocity of the boat.

19 An object is pulled up a slope with a force of 300 N. If theobject moves with a constant speed of 2.0 m/s,

(a) what is the friction on the slope?

(b) using a scaled vector diagram, find Nand W, ignorethe friction of the slope.

20 A rectangular block of metal is 50 mm long, 35 mm wide and has a thickness of 3.0 mm. It weighs

0.15 N. Calculate the density of the metal in kg/m3.

21 A uniform sheet of material has an area of 1.8 m2. It has a mass of 0.15 kg and the material has a

density of 2.5 kg/m3. Find

(a) its thickness;

(b) its weight, if 1.00 kg of the material weighs 10.0 N, on earth;

(c) the area of the material required to make up 1.00 kg.

22 A cube of sides 3.0 cm each has a density of 6.0 g/cm3. A hole of volume 1.0 cm

3is drilled into the

cube. The hole is then filled up with a certain material of density 5.0 g/cm3. Calculate the density of

the composite cube.

f

F

W

N

30

Current

1.0 m/s

B

A


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23 A man is playing golf on a golf course. After being hit, the golf ball with a mass 0.080 kg starts out

with a speed of 50.0 m/s.

(a) Calculate the max height reached.

(b) What is the speed of the ball when it has reached a height of 30.0 m?

(c) The man hits a second golf ball of identical mass. As the ball travels horizontally at a speed

of 15.0 m/s, it hits the leaves of a tree. It then continues to move horizontally for a further

20.0 cm. Find the average resistive force exerted by the leaves of the tree on the ball.

24 A steel ball of mass 80 g is held 1.6 m above a horizontal steel plate,

as shown. The ball is dropped from rest and it bounces on the plate,

reaching a height h. Take g = 10 m/s2.

(a) Calculate the speed of the ball as it reaches the plate.(b) As the ball loses contact with the plate after rebound, the

kinetic energy of the ball is 90% of that before. Calculate

(i) the height hto which the ball reaches;(ii) the speed of the ball as it leaves the plate after rebounce.

(c) Suggest what happens to the 10% of the energy after rebounce.

25 The diagram illustrates the principles of a fair-ground ride. The vehicle starts from rest at point A

which is at the top of the curved track. The vehicle then rolls down the track as far as the point X.

Beyond X, the track is horizontal, and the vehicle is decelerated as it passes through a trough

containing water, coming to rest at point B.

(a) (i) Describe the main energy conversions which take place as the vehicle moves from A

to B.

(ii) As the vehicle moves from A toX, it travels 50 m along the

track and falls through a verticalheight of 10 m. Assume that the

effects of friction can be ignored,

calculate the speed of thevehicle when it reaches point X.

(iii) The vehicle comes to rest in the water 5.0 s after passing X. Determine the average

retarding force exerted by the water on the vehicle.

(b) A designer attempts a more accurate prediction of the speed of the vehicle at Xby assuming

that there is a constant retarding force of 20 N acting on the vehicle caused by the friction in

the wheel bearings.

(i) Calculate the expected speed of the vehicle at X.(ii) Calculate the minimum length of water trough if the depth of the water is such that

the vehicle again comes to rest 5.0 s after passing X.

(c) State and explain whether it is advisable for the designer to include a value for friction in the

calculation of the minimum length of the trough or to assume that the effects of friction can

be ignored.

26 When large buildings are being erected, particularly on softer ground, piles are driven into theground to provide a firmer base. The diagram shows a pile hammer with a mass of 2 500 kg in

operation.

(a) Calculate the loss of gravitational potential energy when the hammer falls 1.80 m to hit thepile.

(b) What is the speed at which the hammer hits the pile?


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(c) The total mechanical energy of the pile andthe hammer just after impact is 27 000 J.

(i) How much energy is lost?(ii) What has happened to the lost energy?

(d) The pile is knocked into the ground a distanceof 10.0 cm. Calculate the average frictional

force exerted on the pile while it is moving

down.

27 The diagram below shows a machine with a conveyor belt that is used to transport bags of cementfrom the ground to the second floor of the building.

(a) Given that the mass of a bag of cement is 20 kg, calculate the work done in transporting abag of cement from the ground to the second floor.

(b) The conveyor belt is able to deliver a bag

of cement to the second floor in 15 s.Assume that no energy is lost to the

surroundings, calculate the power of the

machine.(c) The man on the second floor of the

building decides to play a prank and

throws a bag of cement down.

(i) What is the kinetic energy?

(ii) Calculate the speed of the bag of

cement just before it hits the ground?

28 F ig A shows a gymnast of mass 48.0 kg jumping on a trampoline who can achieve a maximum

height of 5.00 m. F ig Bshows the speed-time graph of her motion on the trampoline.

(a) At which point(s) did she achieve maximum gravitational potential energy?

(b) State and explain the energy changes between point A and C.

(c) Determine the maximum kinetic energy from the graph.

(d) Calculate the power developed by the trampoline on thegymnast between point Cand D.

(e) State one assumption made during your calculation in part (d).

29 A ball rolls off of a table with a horizontal speed of 2.7 m/s. If the table is 1.6 m high,

(a) when does the ball hit the ground?

(b) how far away from the base of the table does the ball travel?

(c) with what vertical velocity does the ball hit the floor?

(d) calculate the final velocity of the ball when it hits the floor.

Pile

hammer

pile

5.0 m

5.00 mSpeed/(m/s)

Time/s

10.0

5.0

1.0 1.3 1.6 2.60

B D

ECA


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30 The diagram shows one form of diving-board used at swimming pools. The board is pivoted at F.A woman of weight 640 N stands still with her centre of gravity directly above a point 1.80 m from

Fas shown. A spring Sholds the diving-board in a horizontal position.

(a) Calculate the moment of the weight of thewoman about F.

(b) Assuming that the distance between the springSand the point F is 0.300 m, calculate the

force exerted by the spring to balance the

weight of the woman.

31 A painter stands on a uniform plank 8 m long and of mass 80 kg.

The plank is suspended horizontally by a vertical ropes attached 1 m

from each end as shown in the diagram. The mass of the painter is 60

kg.

(a) Calculate the tensions T1and T2in each rope when the painter

is 2 m from the centre of the platform and nearer to T1.

(b) State (with no calculation required) how you would expect the

tensions in the rope to vary as the painter moves along theplank from Xto Y.

32 An uniform steelyard, suspended at P, is used for weighing. The weights of the pole and the

counterweight are 5.0 N and 15.0 N respectively.

(a) When the pan is empty, the counterweight is1.0 cm from Pin order to balance the steelyard.

(i) Indicate the line of action of the weight ofthe pole on the diagram.

(ii) What is the weight of the empty pan?(iii) What is the magnitude of the upwardforce exerted on the steelyard at P?

(b) If the pan is slightly heavier, what adjustment to balance the steelyard? Explain your answer.33 The diagram shows a piece of glass being lifted by a suction cup. Some air inside the suction cup is

removed by a vacuum pump. The atmospheric pressure outside the cup prevents the glass from

dropping. The area of the glass covered by the cup is 0.002 5 m2

and the pressure inside the cup is

reduced to 60 kPa. Given that the atmospheric pressure is 100 kPa,

(a) calculate the minimum weight of glass that can belifted with this cup.

(b) state one change that would allow the suction cup tolift a heavier piece of glass.

34 The diagram shows a barrel that contains pressurized air. If the pressure

of the air inside the barrel is 200 kPa, calculate the average force of the

collision of air particles on the inside surface area of the barrel.

35 A lift of mass 2 500 kg moves upwards with an acceleration of 0.70 m/s2. The lift is attached to acable which has a safe tensile stress of 4.5 10

7Pa. The tensile stress of a cable is the tensile force

per unit area of cable. What is the minimum cross-sectional area of the cable that should be used?


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36 A simple mercury barometer is carried to the top of a mountain where the atmospheric pressure is

less than at its base.

(a) Calculate the pressure at the top of the mountain in Pa? (density of mercury is 13 600 kg/m3)(b) Indicate on the diagram with a Z, the point where the pressure is zero.(c) How does the length ofXof the space above the mercury and the pressure in this space,

change as the barometer is taken from the base to the top of the mountain? Explain.

How would the mercury height be

affected if air got into the tube in

position X?(d) What would happen to this reading

if the barometer was tilted at

different positions as shown in thediagram? Indicate on the diagram

the position of the mercury level

inside the tube.

37 The diagram shows a water manometer connected to a gas supply. The difference in height

between the two levels is 28 cm.(a) What would be the difference in height between the two waterlevels if the diameter of the right-hand tube were double that of

the left-hand tube?

(b) If the mercury were used instead of water, what would be thedifference in the height between the levels? (Take density of themercury to be 14 times that of water.)

(c) Give one reason why an astronaut on the moon could not use this manometer for measuring

the pressure of his oxygen supply.

38 The diagram shows a simple U-tube which contains two liquids, waterand mercury. Both ends of the U-tube are open to the atmosphere. The

density of water is 1 000 kg/m3

while that of mercury is 13 600 kg/m3.

Take pressure of atmosphere as 100 kPa and the acceleration due to

gravity as 10 m/s2.

(a) State the pair(s) of points that experience(s) the same pressure.

(b) Calculate the height y.(c) State the total pressure at point Ein Pa.

(d) What is its equivalent in mmHg?

39 The diagram shows a simple hydraulic system used to raise abig rock. The area of small piston is 0.2 m

2while that of the big

piston is 1.2 m2. Calculate the force exerted on the large piston

when a force Fequals to 20 N is applied to the handle.

40 The diagrams show the same glass tube in three different positions. If the atmospheric pressure =76 cmHg,

(a) calculate the length lBof the trappedair column.

(b) what is the length lCof the trappedair column?

55 cm

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