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Glendale College // Spring 2017
Astronomy 110: Homework 5
SOLUTIONS
Newton’s Laws of Motion
(Adapted from materials by J. Krestow, Glendale College.)
Explain Newton’s first law of motion using a specific example from your everyday life:
Aristotle thought that objects preferred to be at rest…even if they were previously moving. Newton’s first
law tells us that this isn’t true—objects actually like to keep doing exactly what it is they’ve been doing (be
it standing still or moving), unless some outside force causes them to do something different.
Your seatbelt provides a great everyday example of Newton’s first law in action. When a car suddenly
stops, people inside the car who are not firmly tethered to it (via a seatbelt) continue doing exactly what
they were doing before…moving forward. The seatbelt conveys the information from the car to your body
that the car is slowing down—in other words, it’s the thing that exerts a force on you.
Now explain Newton’s third law of motion using a specific example from your everyday life:
Newton’s third law tells us about the relationship between the forces acting between a pair of objects.
Namely, it says that if there is some force from object A acting on object B, then there must be an equal
(in terms of magnitude) and opposite (in terms of direction) force from object B acting on object A.
As an everyday example from all of our lives, the force of gravity on the Moon due to the Earth is
equivalent in magnitude to the force of gravity on the Earth due to the Moon. It may seem weird, but it’s
true. And, as we’ll see, it explains both why the Moon stays in orbit around the Earth and why the Earth’s
oceans go through two high tides every day.
According to Newton’s second law of motion, F
= m a ↔ a = F/m, where F represents the force
(measured in units called Newtons—abbreviated “N”), m represents the mass of an object (measured in kg),
and a represents the acceleration of that object (measured in meters per second per second—or m/s2).
Calculate the force necessary to accelerate a 600 kg object at a rate of 3 m/s2. Please be sure to show and/
or explain how you arrive at your answer. And be sure to include correct units in your answer!
Newton’s second law states: F = m a. In this problem, m = 600 kg and a = 3 m/s2. The force, F, is
therefore given by:
F = m • a = 600 kg • 3 m/s2 = 1,800 kg•m/s2 = 1,800 N
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If 500 N of force is applied to a 6 kg object, what would its acceleration be? Again, be sure to show how you
arrive at your answer and to provide proper units for that answer.
Newton’s second law (turned around from its traditional form) states: a = F / m. In this problem, m = 6 kg
and F = 500 N. The acceleration, a, is therefore given by:
a = F / m = 500 N / 6 kg ≈ 83.3 m/s2
If 90,000 N of force can accelerate a body to 90 m/s2, what is the mass of that object? Newton’s second law states: F = m a. We can divide both sides by the acceleration, a, to find the
relationship: m = F / a. In this problem, F = 90,000 N and a = 90 m/s2. The mass, m, is therefore given by:
m = F / a = 90,000 N / 90 m/s2 = 1,000 kg
What might this object be? (Try to figure out what everyday object is about this mass.)
1,000 kg is roughly the mass of a compact car.
Newton’s Law of Universal Gravitation
According to Newton’s law of gravity, if the mass of the Moon were to somehow instantaneously double, how
would the gravitational force on it due to the Earth be affected?
The gravitational force on the Moon would double.
Would the Moon’s acceleration change? How much?
The Moon’s acceleration would actually NOT change at all.
This is a rather amazing fact. The gravitational force would
increase, but the Moon’s increased inertia (due to its
increased mass) exactly balances this out, and Newton’s
2nd law tells us that its acceleration would be unchanged.
Would the gravitational force on the Earth due to the Moon be affected? How?
The gravitational force on the Earth due to the Moon would also be doubled.
If the Moon “jumped” to half its current distance, how would the gravitational force on it from Earth change?
The gravitational force between two objects depends on the inverse square of the distance
between them. Therefore, halving the distance between two objects increases the gravitational
force by 22 = 4 times.
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What Does It Mean to Orbit?
Imagine that a spacecraft somehow appears out of nowhere at the exact halfway point between the Earth
and Moon. Initially, the spacecraft is completely stationary with respect to both celestial bodies, like this:
According to Newton’s laws of motion and his law of gravity, what will happen to the spacecraft? Draw the
path of the spacecraft’s trajectory on the above drawing, and describe why this will happen below.
According to Newton’s law of gravity, the gravitational force between two objects depends upon the
masses of the objects and (the square of) the distance between them. In this scenario, since the distance
from the spacecraft to the Earth and Moon is the same, the only factor determining the gravitational force
between the objects are their masses. Since the Earth is more massive than the Moon, the gravitational
force on the spacecraft from the Earth will be greater than the force from the Moon. Newton’s second law
tells us that an object will accelerate under the influence of a net force. Thus, the spacecraft will
accelerate (start speeding up) towards the Earth, and eventually smack right into it.
Is there a location between the Earth and Moon where the spacecraft could pop into existence and remain
there forever? (Hint: There is.) Indicate where this is in the following drawing.
(This is the approximate location. The point is that it has to be
closer to the Moon than Earth since the Earth is a lot more
massive. Being closer to the Moon makes up for that since the
gravitational force decreases with the square of the distance.)
Why wouldn’t the spacecraft move if it was in this location?
At this location, the gravitational force between the two celestial objects would be equal in magnitude
(i.e., size) and opposite in direction. Newton’s second law of motion says that an object will accelerate if
there is a net force acting on it. Since the force of gravity from the Earth and Moon balance at this
location, there is no net force…and thus the spacecraft will remain at rest.
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