Sample Question 1: A lunar exploration vehicle was made by a research team, and it weighs about
six times more than it will on the moon. In order to have the same acceleration on the moon as well
as on the Earth, what will be the net force acting on the vehicle? Will it be greater than, less than, or
the same as that required on Earth?
Solution: According to Newton’s second law, the net force is F = ma. Here, m is the vehicle’s mass
and a is the acceleration. The net force depends on the mass for a constant acceleration. Here, the
mass of the vehicle is constant. Therefore, the same net force would be required.
Sample Question 2: You and your friend are pushing a box in the same direction. Its mass is 200
kg. You apply 20 N to the box, while your friend applies 30 N. A force created by friction is 40 N in the
opposite direction. What is the acceleration of the box?
Solution: There are three forces acting in this system, and the net force should be added up. Two of
them are acting toward the same direction, and the remaining is acting in the opposite direction, as
you can see below. Thus, the net force F = 30 N + 20 N – 40 N = 10 N. From Newton’s 2nd law, F =
ma. The mass of box is given by 200 kg. Therefore, the acceleration a = F / m = 10 N / 200 kg = 0.05
m/s2
PHY 1301, Physics I 4
UNIT x STUDY GUIDE
Title
The third law is the law of action–reaction. The forces exist in pairs. The magnitudes of forces are
equal, but their directions are opposite (Shipman et al., 2009). That is, every action has an equal and
opposite reaction. For example, when you push a wall on a slippery floor, you feel that your feet are
moving backward. The push force exerted by you is the same as that by the wall. That is, the two
forces are equal in magnitudes, but opposite in direction. Review Example 4 on p. 87 in the textbook
(Cutnell et al., 2018).
Free Fall
Every object on Earth falls downward because of Earth’s gravity. Earth’s gravity points to the center of Earth.
If there is no air, all of the falling objects should experience the same acceleration. Recall from the Unit I
Lesson that in order to prove this, an astronaut, David Scott of the Apollo 15 mission, performed the
experiment on the moon.
When we ignore the air resistance and assume the constant acceleration, we say that the falling object is in
free fall. The acceleration of the freely falling body is due to gravitational acceleration g, and it is about 10
m/s2 on the surface of the Earth. However, the object is at considerably high altitude, the acceleration due to
gravity is not constant. The gravitational acceleration is inversely proportional to the square of the distance
from the center of the Earth to the object.
The Fundamental Forces
All the different forces observed in nature can be explained in terms of four basic interactions that occur
between elementary particles: gravitational force, electromagnetic force, strong nuclear force, and weak
nuclear force. The associated particles for the strong force are mainly gluons and pi nucleons.
The main role of the strong force is to hold the nuclei of atoms together. Principally, it is attractive; however, it
can sometimes act in a repulsive way with proper conditions. The strong nuclear interaction has a very
powerful strength of the force, but it is very short–ranged (about 10–13 cm). The attractive force only works well
within the size of the nucleus. The role of a neutron is very important to maintain the structure of the nucleus.
A repulsive force exists between two protons because they have the same charge. Remember that in the
influence of electrostatic force two like charges repel, and two opposite charges attract. Thus, more neutrons
than protons are needed to keep the stable nucleus as the atomic number increases. The maximum proton
number is 83 with 126 neutrons for the stable structure in nature. All nuclei that have an atomic number
greater than 83 are unstable because the binding force to hold the nuclei is weak and disintegrates or
rearranges its structure. This is known as radioactivity. The radioactive decay or neutrino interactions can be
explained by the weak force, and its strength is weak with a short range. The associated particles for the
weak nuclear force are known as intermediated vector bosons such as W+, W–, and Z0. They are spin 1
particles, and their masses are greater than 80 GeV.
Sample Question 3: An astronaut pushes on the spacecraft with a force of 40 N near the
International Space Station. His mass is 90 kg, and the spacecraft’s mass is 10,000 kg. What are
the accelerations of the space craft and the astronaut?
Solution: According to Newton’s third law, when the astronaut applies the force to the spacecraft,
the spacecraft also applies the same amount of force to the astronaut. That is, the magnitudes of
the two forces are identical, but the directions are different.
From the second law of Newton, the acceleration of the spacecraft is as = 40 N / 10,000 kg = 0.004
m/s2. The acceleration of the astronaut is aa = –40 N / 90 kg = –0.44 m/s2. Note that the magnitudes
of the action and reaction forces are always equal, but they do not have the same acceleration
unless they have the same mass.