1. The fundamental force that: (4 marks)
____ 1. causes hair to stand on end after being
rubbed by a balloon a) strong nuclear
____ 2. causes protons to remain in the nucleus
despite repulsive forces b) weak nuclear
____ 3. controls the planets' orbit around the sun c) electromagnetic
____ 4. ensures light doesn’t emerge from a black
hole d) gravitational
____ 5. is responsible for fusion on the sun
____ 6. changes a proton into a neutron
____ 7. is responsible for residual colour force
(colour force holds quarks together)
____ 8. is responsible for the aurora borealis
2. A 1.20 x 105 kg exploratory satellite in orbit around the Jupiter wants to increase its orbit from
1.00 x 105 m above the surface to 2.00 x 105 m above the surface. Determine the amount of
energy required to move orbits. (3 marks)
3. A 5.50 x 104 kg rocket is launched from the surface of the Earth with a speed of 888 m/s.
Determine its maximum height. (4 marks)
4. Determine the orbital speed of the moon and the value of the gravitational field on its surface
(neglect any field effects due to the Earth). (4 marks)
5. Determine the force of repulsion between two alpha particles located 5.0 x10-5 m apart. Note
that an alpha particle is a helium nucleus (2 protons, 2 neutrons) with the electrons stripped
away. (2 marks)
6. A proton with a mass of 1.67 x 10-27 kg is released from rest from the positive plate in a
parallel plate apparatus. If the voltage applied to the plates is 350 V, determine the velocity of the
proton just before it hits the negative plate. (3 marks)
the options for #1 are a) strong nuclear , b) weak nuclear, c) electromagnetic, d) gravitational
well electrostatic force causes hair to stand on end
and gravity keeps the planets in orbit by the way
1. The correct answers for the fundamental forces are:
- 1. causes hair to stand on end after being rubbed by a balloon: c) electromagnetic
- 2. causes protons to remain in the nucleus despite repulsive forces: a) strong nuclear
- 3. controls the planets' orbit around the sun: d) gravitational
- 4. ensures light doesn’t emerge from a black hole: d) gravitational
- 5. is responsible for fusion on the sun: a) strong nuclear
- 6. changes a proton into a neutron: b) weak nuclear
- 7. is responsible for residual colour force (colour force holds quarks together): a) strong nuclear
- 8. is responsible for the aurora borealis: c) electromagnetic
2. The energy required to move the satellite from 1.00 x 10^5 m to 2.00 x 10^5 m above the surface of Jupiter can be determined using the formula:
ΔE = (G * M * m) * (1/r_initial - 1/r_final)
where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), M is the mass of Jupiter (1.90 x 10^27 kg), m is the mass of the satellite (1.20 x 10^5 kg), r_initial is the initial distance from the center of Jupiter (1.00 x 10^5 m), and r_final is the final distance from the center of Jupiter (2.00 x 10^5 m).
Calculating:
ΔE = (6.67 x 10^-11 Nm^2/kg^2 * 1.90 x 10^27 kg * 1.20 x 10^5 kg) * (1/1.00 x 10^5 m - 1/2.00 x 10^5 m)
ΔE = 1.81 x 10^16 J
Therefore, the amount of energy required to move orbits is 1.81 x 10^16 Joules.
3. To determine the maximum height of the rocket, we can use the principle of conservation of mechanical energy.
The initial kinetic energy (KE) of the rocket at the surface of the Earth is given by:
KE_initial = (1/2) * m * v^2
where m is the mass of the rocket (5.50 x 10^4 kg) and v is the launch speed (888 m/s).
At the maximum height, all the initial kinetic energy is converted into gravitational potential energy (PE):
PE_max = m * g * h_max
where g is the acceleration due to gravity on Earth (9.8 m/s^2) and h_max is the maximum height.
Setting KE_initial equal to PE_max:
(1/2) * m * v^2 = m * g * h_max
Simplifying:
h_max = (1/2) * v^2 / g
h_max = (1/2) * (888 m/s)^2 / (9.8 m/s^2)
h_max = 40,804.08 m
Therefore, the maximum height of the rocket is 40,804.08 meters.
4. The orbital speed of the moon can be calculated using the formula:
v_orbit = √(G * M / r)
where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), M is the mass of the celestial body (in this case, the Earth), and r is the radius of the orbit.
The average distance between the Moon and the Earth is approximately 3.84 x 10^8 m.
Calculating:
v_orbit = √(6.67 x 10^-11 Nm^2/kg^2 * 5.97 x 10^24 kg / 3.84 x 10^8 m)
v_orbit = 1,022 m/s
The value of the gravitational field on the surface of the Moon can be calculated using the formula:
g = (G * M) / r^2
where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), M is the mass of the Moon (7.35 x 10^22 kg), and r is the radius of the Moon (1.74 x 10^6 m).
Calculating:
g = (6.67 x 10^-11 Nm^2/kg^2 * 7.35 x 10^22 kg) / (1.74 x 10^6 m)^2
g = 1.63 m/s^2
Therefore, the orbital speed of the Moon is 1,022 m/s and the value of the gravitational field on its surface is 1.63 m/s^2.
5. The force of repulsion between two alpha particles located 5.0 x 10^-5 m apart can be calculated using Coulomb's law:
F = (k * q1 * q2) / r^2
where k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the alpha particles (both have a charge of 2e, where e is the elementary charge), and r is the distance between the particles.
Calculating:
F = (9 x 10^9 Nm^2/C^2 * (2 x 1.6 x 10^-19 C)^2) / (5.0 x 10^-5 m)^2
F = 4.59 N
Therefore, the force of repulsion between the two alpha particles is 4.59 Newtons.
6. The velocity of the proton just before it hits the negative plate can be determined using the principle of conservation of energy.
Assuming the parallel plates are perpendicular to the direction of motion of the proton, the change in electrical potential energy (ΔPE_electric) can be calculated as:
ΔPE_electric = q * V
where q is the charge of the proton (1.6 x 10^-19 C) and V is the applied voltage (350 V).
The change in kinetic energy (ΔKE) is equal to the initial kinetic energy (KE_initial) since the proton starts from rest:
ΔKE = KE_initial = (1/2) * m * v_initial^2
where m is the mass of the proton (1.67 x 10^-27 kg) and v_initial is the initial velocity.
Setting ΔPE_electric equal to ΔKE:
q * V = (1/2) * m * v_initial^2
Solving for v_initial:
v_initial = √(2 * q * V / m)
v_initial = √(2 * 1.6 x 10^-19 C * 350 V / 1.67 x 10^-27 kg)
v_initial = 7.68 x 10^5 m/s
Therefore, the velocity of the proton just before it hits the negative plate is 7.68 x 10^5 meters per second.