Worksheet: Newton’s Laws of motion
Formulas
Fres = resultant force, N
m = mass, kg
g = gravitational constant
s = distance. m
u = initial velocity, m s-1
v = final velocity, m s-1
a = acceleration, ms-2
t = time
𝐹𝑟𝑒𝑠 = 𝑚𝑎
𝐹𝑤𝑒𝑖𝑔ℎ𝑡 = 𝑊 = 𝑚𝑔
𝑠 = 𝑣𝑡
𝑣−𝑢
∆𝑣
𝑎=
=
1
𝑡
𝑡
𝑠 = (𝑢 + 𝑣)𝑡
2
1
𝑠 = 𝑢𝑡 + 𝑎𝑡 2
2
𝑣 = 𝑢 + 𝑎𝑡
𝑔 = 10 ms-2 (unless otherwise stated)
only for constant velocity during t
only for constant acceleration during t
only for constant acceleration during t
only for constant acceleration during t
only for constant acceleration during t
Steps for solving science questions with calculations:
QuQuDECA
1. Question, Quantity and Unit: Highlight what is being asked and write down the quantity and unit.
2. Data. Underline and copy data; numbers with units, formulas, situation sketches in the question
3. Extra / equation. Write down extra data; situation sketches, equations and constants that you need
4. Calculation. Perform the calculations, and write the calculations down.
5. Answer check. Write down the answer and check, QuQu; quantity, unit and significant figures.
Example: What force must be acting on a mass of 6 kg in order to produce an
acceleration of 7.9 ms-2 ?
1.
2.
3.
4.
5.
QuQu:
Data:
Extra:
Calculation:
Answer check:
force, F, newton, N
mass = m = 6 kg
Fres=ma
Fres = 6 x 7.9 = 47.4
Force is 47 N
acceleration = a = 7.9 ms-2
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Section A: Short Questions
1. What force must be acting on a mass of 4 kg in order to produce an acceleration of 4.9 ms-2 ?
2. What acceleration is produced on a car with mass 2000 kg by a force of 500 N?
3. A mass of 60 kg is acted on by a force of (a) 6N and (b) 1000 N. For a and b, what is the
acceleration?
4. What must be the mass of a truck if it moves with an acceleration of 5 ms-2 under the action
of a force of (a) 300 N and (b) 490 N
5. A car of mass 1000 kg travelling at 20 ms-1 is has a stopping distance of 25 m. What uniform
force does the brake exerts?
6. A boy and his bicycle together have a mass of 70 kg. What must be the force propelling the
bicycle forward if the acceleration is 0.7 ms-2?
7. A locomotive of a train exerts a force of 49000 N. The mass of the train is being 300 x 103 kg.
Find the acceleration of the train, given that the motion is opposed by a frictional force of 137.2
N per 1000 kg mass of the train.
8. A lorry of mass 2000 kg is travelling at 9 km h-1. It is being accelerated by a force of 1372 N for
20 seconds. What is its speed in km h-1 after 20 s?
9. Assuming that the brakes of a motor car can producing a deceleration force equal to half the
weight of the car. What is the shortest distance in which a car travelling at 48 km h-1 can be
stopped?
10.
If a man of mass 70 kg traveled to another planet where
the gravity is 1.4 ms-2. What would be his
(a) original weight?
(b) his new weight?
11.
The engine of a 900 kg car suddenly stops when the car
is travelling at 72 km h-1. The car driver does not use the brake. The
car stops after travelling a distance of 80 m. Calculate the average
resultant force that causes the car to stop. (The resultant force is
due to friction and air resistance)
12.
A balloon of total mass of 1000 kg floats motionless over
the earth’s surface. If 100 kg of sand ballast is thrown overboard
沙碴被抛入船外, with what acceleration does the balloon start to
rise and what will be its velocity after 9 seconds. Take gravity = 9.81
ms-2 .
13.
A champion tennis player’s fastest serve 发球 has been
estimated as having a velocity of 160 km h –1. What force does the
tennis net 网球网 exert in stopping such a serve in 0.2 m? Mass
of the tennis ball = 0.05 kg.
14.
A crane rope can withstand a tension 起重绳索可以承
受 拉 力 of 1176 N without breaking. What is the greatest
acceleration with which the rope can raise a crate of mass 100 kg?
15.
A balloonist 气球手 estimates the motion of the balloon
by hanging a mass of 7 kg at the end of a spring balance 弹簧平衡.
The spring balance reads 85 N. What is the acceleration of the
balloon? Can you tell if it’s going up or down?
16.
An elevator of a coal mine 煤矿 starts to go down with an acceleration of 1 ms-2
(situation 1). After a while it has a speed of 12 ms-1. The elevator keeps this speed for some time
(situation 2). Then it slows down with an acceleration of -2 ms-2 (situation 3). Find for all 3
situation the force exerted on the floor of the cage by the mine workers. The total mass of the
mine workers is 1000 kg.
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17.
A trolley of mass 1 kg, pulled along a frictionless
surface 无摩擦表面 by two elastic threads in parallel, is found
to travel a distance of 1 meter from rest in 5 seconds. What is
(a) the acceleration of the trolley
(b) the force exerted by the threads?
18.
A motionless mass of 6 kg on a smooth horizontal
table is connected to a mass of 1 kg, by a string over the edge
of the table. Find
(a) the acceleration of the system
(b) the tension in the string.
19.
A trolley of mass 2 kg is pulled along a table by a string
attached to a mass of 25g hanging downwards. The trolley is observed to pass over 2.18 m in 6
s from rest. Calculate the value of gravity.
20.
A block of 1 kg is placed 1 m from the edge of a smooth horizontal table which is 0.7 m
high. This weight is connected by an in-extensible string to a mass of 0.25 kg, which hangs just
over the edge of the table. Find the time it takes for the heavier mass reaches the edge. (Very
difficult question, read carefully, and make a situation sketch!)
21.
A rope is placed over a smooth pulley. A sack of flour of mass 140 kg is attached to one
end of the rope and a man of mass 70 kg holds on the other end. Find
(a) the acceleration with which the man is lifted through the air
(b) the tension in the rope
(c) the distance the man raise in 3 s.
22.
Two scale pans each of mass 30g are attached to a thread which passes over a smooth
pulley. Mass X of 300g is placed in one pan and mass Y of 120g is placed onto the other. Find
(a) the acceleration of the system
(b) the tension in the thread
(c) the reaction force each mass exerted on the pan
23.
The gravitational acceleration of Earth, Moon and Jupiter are 10 ms-2, 1.6 ms-2 and 24.3
-2
ms respectively.
(a) What is the weight of a 0.5 kg mass on Moon.
(b)
The weight of an astronaut on Earth is 750 N. What is the mass of the astronaut ?
(c) What is the weight of the astronaut on Jupiter ?
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Section B Conventional Questions
24. Jane is holding a 5 kg mass which is connected to a 1 kg mass by a
string as shown in below diagram.
(a) What is the resultant force on the 1 kg mass?
(b) What is the tension in the string when the 5 kg block is held by Jane’s hand ?
(c) Now Jane releases the 5 kg block and let both the 5 kg and 1 kg block free falls under gravity.
(i)
(ii)
(iii)
(iv)
What is the acceleration of the 5 kg block ?
What is the acceleration of the 1 kg block ?
What is the resultant force on the 1 kg mass ?
What is the tension in the string ?
(d) Explain your answer in (c. iv) briefly.
25. Joan has a mass of 50 kg and stands on a balance in a lift moving upwards from rest.
(a)
Draw the free body diagram of Joan when the lift is at rest.
(b) Complete the following table
Reading of the scale
(< or > 500 N)
Weight that Joan feels
(Heavier, lighter or
normal )
=500 N
Normal
Lift accelerates upwards
Life moving up at constant
speed
Lift slows down and stops
(c) Find the reading of the scale in the following case
(i)
the lift accelerates upwards at 3 ms-2
(ii)
the lift moves up with a uniform velocity of 5 ms-1
(iii) the lift moves up but decelerates at 2 ms-2.
26. Two connected boxes are at rest in a smooth surface and Mary applies a force of 50 N to pull
the 10 kg box to the right. It is given that the two boxes accelerate with the same acceleration.
(a) What is the acceleration ?
(b) Draw the free body diagram of the 30 kg box
(c) Draw the free body diagram of the 10 kg box
(d) What is the magnitude of tension in the string between the two boxes?
(e) Hence, or otherwise, find the resultant force acting on the 10 kg box.
(f) The string connecting the boxes breaks suddenly. Mary worries if the 30 kg box would stops.
Comment on her worry.
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Jackie dives from an airplane to the ground at 6000 m above the ground and he opens
his parachute.
(a) Draw the free body diagram to show all the forces acting on Jackie when he falls.
(b)
How will the force(s) change with time?
(c )
Will Jackie falls with constant speed eventually ? Explain briefly.
27.
28.
*Bonus question: A trolley of mass 2 kg is initially at rest on an inclined plane. The angle
of inclination is 30o. After a push of 0.05 s, it runs down a friction-compensated runway ( i.e mg
sinθ = friction ) at a constant speed of 0.8 ms-1 .
(a) Calculate the force of initial push on the trolley.
(b)
What is the frictional force acting on the trolley ?
(c) The trolley is then pushed again upwards along slope from the slope’s bottom from rest until
its speed is 6 ms-1 upward along slope. The pushing force is then released.
(i) What is the acceleration of the trolley after the pushing force has been released ?
(iii)
Find the distance that the trolley can travel along the slope before it reaches the
highest position.
29.
*Bonus question. With a string Victor pulls a small wooden box of weight 12 N to move
with a uniform velocity on a rough horizontal ground. The friction acting on the wooden box by
the ground is 4 N.
(a) Draw the free body diagram to show all the forces acting on the box.
(b)
Find the tension T in the string
(c) Find the contact force R acting onto the box by the ground.
(d)
If Victor pulls the box with a longer string but the same tension as in (b), how would R
changes ? Explain your answer briefly.
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30. *Bonus question. Refer to the following diagram, θ= 30o , m1 = 2 kg and m2 = 5 kg. The slope is smooth
and friction is negligible and the pulley is light and smooth. The string connecting both masses is light and
in-extensible.
(a) Draw the free body diagram of mass m1
(b) Draw the free body diagram of mass m2.
(c) If the system is released from rest, what is the acceleration of
(i)
the mass m1 and
(ii)
the mass m2
(d) If the friction between the mass m1 and slope is so big that after release both masses m1 and m2
remains at rest. Find
(i)
(ii)
acceleration of m1 and m2
the tension in the string.
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Answersheet
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3
19.6 N
0.25 ms-2
a. 0.1 ms-2
b. 16.7 ms-2
4
a.
b.
5
6
7
8
9
10
8000 N
49 N
0.261
58.4 km h-1
17.8 m
a. 700N
b. 98N
2250 N
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Acceleration 1.09 ms-2,
Velocity: 9.81 ms-1
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246.9 N
1.76 ms-2
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60kg,
98kg
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acceleration of 2.14 ms-2 upwards
9000 N, 10000 N, 12000 N
a. 0.08ms-2
b. 0.08 N
a. 1.43 ms-2
b. 8.57 N
9.81 ms-2
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a.
b.
c.
a.
b.
c.
3.33 ms-2 upwards,
933 N,
15 m
3.75 ms-2,
2.06 N,
Mass X 1.88 N, mass Y 1.65 N
a.
0.8 N
b. 75 kg
c.
1820 N
a.
0N
b. 10 N
c.
i. 10 ms-2 downwards ii. 10 ms-2 iii. 10 N
downwards iv. 0 N
d. if the tension is not zero, then the
resultant force in 5 kg and 1 kg mass will no
longer equal to their weight and they cannot
undergo free falling
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c.
i. 650 N ii. 500 N iii. 400 N
a.
1.25 ms-2
d. 37.5 N
e.
12.5 N
f.
Mary should not worry. The box will not
stop. Due to Newton’s first law a moving object
will never stop if there is no resultant force
acting on it.
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b. weight is constant, air friction increases
with time
c.
Yes. Because eventually the air resistance
will equal to weight, therefore there is no
resultant force on Jackie
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a.
32 N
b. 10 N, upwards along slope
c.
i. 10 ms-2 downwards along slope ii. 1.8 m
b. 8 N
c. 5.07 N, upwards
d. R will be bigger since θ increase, the
vertical component of T decreases, hence R
increases. Since R plus vertical component of T
must equal to weight of box.
1.03 s
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c.
d.
i. 5.71 ms-2 upwards along slope
ii. 5.71 ms-2 downwards
i. 0 ms-2
ii. 50 N
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