Trimester Three 2022 Examination
USEFUL FORMULAE AND DATA
Physical Constants
g = 9.8 ms−2 , h = 6.63 × 10−34 Js , R = 1.097 × 107 m−1 , c = 3.0 × 108 ms −1
me = 9.11 × 10−31 kg , mp = 1.67 × 10−27 kg , Charge of the electron e = −1.6 × 10−19 C
G = 6.67 × 10−11 Nm2 kg −2 , Speed of sound in air v = 340.0 ms−1 𝑀𝐸𝑎𝑟𝑡ℎ = 5.98 × 1024 𝑘𝑔
𝑅𝐸𝑎𝑟𝑡ℎ = 6.38 × 106 𝑚
Newtonian Mechanics
I = ∫ Fdt , ⃗ ,
τ⃗ = r × F τ = Iα v = rω, a = rα , ⃗ =r × p
L ⃗ , L = Iω ,
1 2 1 2 W Mm
Icylinder = Idisk = Mr , I = ∑ mi ri2 , K rot = Iω P = , T2 ∝ r3 , F=G
2 2 t r2
Oscillations and Waves
K
x = A cos(ωt + ∅0 ) , v = −Aω sin(ωt + ∅0 ) , a = −Aω2 cos(ωt + ∅0 ) , ω = √m,
−bt −t
E = K + U = ½ kA2 , x = A exp ( 2m ) cos(ωd t) , ω = 2πf, xmax (t) = A exp ( τ )
2π
Travelling waves : y = A cos[kx ± ωt + φ] , Standing waves : y = [2A sin kx] cos ωt , k =
λ
ω T E 1
v= , v = fλ, v=√ =√ , Pmean = μ v ω2 A2 , d sin θ = mλ m = 0,1,2, ..
k μ ρ 2
λL mLλ 1 mLλ
Δy = , ym = , 2nt = (m + ) λ , a sin θ = mλ m = 0,1,2, …, ym =
d d 2 a
v ± v0 I
f ' =f ( ), B = 10 log ( ) dB, where Iref = 10−12 W m−2 , n1 sin θ1 = n2 sin θ2
v∓ vs Iref
1 1 1 q
= + , M = −( )
f p q p
Quantum Physics
13.6 2
Energy levels in a hydrogen-like atom: E = − Z eV (n = 1,2,3, … )
n2
1 1 1 hc K max
= 𝑅𝐻 [ 2 − 2 ] , E = hf = , Vstop = , K max = hf − W,
λ nf 𝑛𝑖 λ e
1240
Ephoton = eV
λ(nm)
h h
1 eV = 1.6 × 10−19 J, λ = p , ∆K = Q∆V, me ≪ mp , ∆x ∆p ≥ ,
4π
h2
En = n2 (8mL2) (n = 1,2,3, … ), Energy levels for an infinite 1-dimensional square well.
, Section A: NEWTONIAN MECHANICS
(25 marks)
QUESTION A1 (1+1+1+1 = 4mark)
(a) A woman is straining to lift a large crate, without success because it is too heavy. We denote the forces on the crate as
follows: P is the upward force the woman exerts on the crate, C is the vertical contact force exerted on the crate by the
floor, and W is the weight of the crate. How are the magnitudes of these forces related while the woman is trying
unsuccessfully to lift the crate?
A) P + C > W
B) P + C < W
C) P = C
D) P + C = W
(b) A Ping-Pong ball moving east at a speed of 4 m/s, collides with a stationary bowling ball. The Ping-Pong ball bounces back
to the west, and the bowling ball moves very slowly to the east. Which object experiences the greater magnitude impulse
during the collision?
A) Neither; both experienced the same magnitude impulse.
B) the Ping-Pong ball
C) the bowling ball
D) It's impossible to tell since the velocities after the collision are unknown.
(c) A potential energy function for system 1 is given by 𝑈1 (𝑥) = 𝐶𝑥 2 + 𝐵𝑥 3 . The potential energy function for system 2 is
given by 𝑈2 (𝑥) = 𝐴 + 𝐶𝑥 2 + 𝐵𝑥 3 , where A is a positive quantity. How does the force on system 1 relate to the force on
system 2 at a given position?
A) The force on the second system will be with greater than the force on the first system.
B) There is no relationship between the forces on the two systems.
C) The force is identical on the two systems.
D) The force on the two systems will be in opposite directions.
E) The force on the second system will be with less than the force on the first system.
(d) On a smooth horizontal floor, an object slides into a spring which is attached to another mass that is initially stationary.
When the spring is most compressed, both objects are moving at the same speed. Ignoring friction, what is conserved during
this interaction?
A) momentum and kinetic energy
B) kinetic energy only
C) momentum and mechanical energy
D) momentum only
E) momentum and potential energy
Page 2 of 10
USEFUL FORMULAE AND DATA
Physical Constants
g = 9.8 ms−2 , h = 6.63 × 10−34 Js , R = 1.097 × 107 m−1 , c = 3.0 × 108 ms −1
me = 9.11 × 10−31 kg , mp = 1.67 × 10−27 kg , Charge of the electron e = −1.6 × 10−19 C
G = 6.67 × 10−11 Nm2 kg −2 , Speed of sound in air v = 340.0 ms−1 𝑀𝐸𝑎𝑟𝑡ℎ = 5.98 × 1024 𝑘𝑔
𝑅𝐸𝑎𝑟𝑡ℎ = 6.38 × 106 𝑚
Newtonian Mechanics
I = ∫ Fdt , ⃗ ,
τ⃗ = r × F τ = Iα v = rω, a = rα , ⃗ =r × p
L ⃗ , L = Iω ,
1 2 1 2 W Mm
Icylinder = Idisk = Mr , I = ∑ mi ri2 , K rot = Iω P = , T2 ∝ r3 , F=G
2 2 t r2
Oscillations and Waves
K
x = A cos(ωt + ∅0 ) , v = −Aω sin(ωt + ∅0 ) , a = −Aω2 cos(ωt + ∅0 ) , ω = √m,
−bt −t
E = K + U = ½ kA2 , x = A exp ( 2m ) cos(ωd t) , ω = 2πf, xmax (t) = A exp ( τ )
2π
Travelling waves : y = A cos[kx ± ωt + φ] , Standing waves : y = [2A sin kx] cos ωt , k =
λ
ω T E 1
v= , v = fλ, v=√ =√ , Pmean = μ v ω2 A2 , d sin θ = mλ m = 0,1,2, ..
k μ ρ 2
λL mLλ 1 mLλ
Δy = , ym = , 2nt = (m + ) λ , a sin θ = mλ m = 0,1,2, …, ym =
d d 2 a
v ± v0 I
f ' =f ( ), B = 10 log ( ) dB, where Iref = 10−12 W m−2 , n1 sin θ1 = n2 sin θ2
v∓ vs Iref
1 1 1 q
= + , M = −( )
f p q p
Quantum Physics
13.6 2
Energy levels in a hydrogen-like atom: E = − Z eV (n = 1,2,3, … )
n2
1 1 1 hc K max
= 𝑅𝐻 [ 2 − 2 ] , E = hf = , Vstop = , K max = hf − W,
λ nf 𝑛𝑖 λ e
1240
Ephoton = eV
λ(nm)
h h
1 eV = 1.6 × 10−19 J, λ = p , ∆K = Q∆V, me ≪ mp , ∆x ∆p ≥ ,
4π
h2
En = n2 (8mL2) (n = 1,2,3, … ), Energy levels for an infinite 1-dimensional square well.
, Section A: NEWTONIAN MECHANICS
(25 marks)
QUESTION A1 (1+1+1+1 = 4mark)
(a) A woman is straining to lift a large crate, without success because it is too heavy. We denote the forces on the crate as
follows: P is the upward force the woman exerts on the crate, C is the vertical contact force exerted on the crate by the
floor, and W is the weight of the crate. How are the magnitudes of these forces related while the woman is trying
unsuccessfully to lift the crate?
A) P + C > W
B) P + C < W
C) P = C
D) P + C = W
(b) A Ping-Pong ball moving east at a speed of 4 m/s, collides with a stationary bowling ball. The Ping-Pong ball bounces back
to the west, and the bowling ball moves very slowly to the east. Which object experiences the greater magnitude impulse
during the collision?
A) Neither; both experienced the same magnitude impulse.
B) the Ping-Pong ball
C) the bowling ball
D) It's impossible to tell since the velocities after the collision are unknown.
(c) A potential energy function for system 1 is given by 𝑈1 (𝑥) = 𝐶𝑥 2 + 𝐵𝑥 3 . The potential energy function for system 2 is
given by 𝑈2 (𝑥) = 𝐴 + 𝐶𝑥 2 + 𝐵𝑥 3 , where A is a positive quantity. How does the force on system 1 relate to the force on
system 2 at a given position?
A) The force on the second system will be with greater than the force on the first system.
B) There is no relationship between the forces on the two systems.
C) The force is identical on the two systems.
D) The force on the two systems will be in opposite directions.
E) The force on the second system will be with less than the force on the first system.
(d) On a smooth horizontal floor, an object slides into a spring which is attached to another mass that is initially stationary.
When the spring is most compressed, both objects are moving at the same speed. Ignoring friction, what is conserved during
this interaction?
A) momentum and kinetic energy
B) kinetic energy only
C) momentum and mechanical energy
D) momentum only
E) momentum and potential energy
Page 2 of 10
