When you think of force you may think of the movie Star Wars and the funny physics pun "May the mass times acceleration be with you." It is a play on words of the famous quote from the movie "May the force be with you." "The force" is the heart of the Star Wars universe. It gives the Jedi their powers, it is well known in Star Wars as an energy field created by all living things. As Obi-Wan once explained to Luke Skywalker "it surrounds us, it penetrates us, it binds the galaxy together". Likewise, the forces of physics are at play in every moment of our lives from sticking a magnet on a fridge door to throwing a ball into a basketball hoop. We will review forces in physics and learn more about pulling forces in this article.
Pulling Force Definition
In the simplest terms, a force is a push or a pull. In basic mechanics, we distinguish between these two by comparing the direction of the force vector acting on an object to the direction of the object's motion. If the force applied aligns with the direction of the object's motion, we call it a pushing force:
A pushing force is a force that aligns with the direction of the object's resulting state of motion.
Even if an object is initially at rest, we regard the force applied to an object to get it to move as a pushing force because the direction of the force vector aligns with the vector of the object's resulting velocity.
In contrast to a pushing force, the notion of a pulling force is a bit more subtle. The reason for this is that we may distinguish between two types of pulling forces: contact pulling forces or long-range pulling forces. A contact pulling force, as the name implies, is one in which the agent responsible for exerting the force on the object is in direct contact with it. For example, pulling on a rope attached to a cart to bring it towards you would be an example of a contact pulling force. What about a long-range pulling force, then? For this, we need to make a small digression into the fundamental interactions in physics.
There are four known fundamental interactions in nature: gravitational, electromagnetic, weak, and strong. Focusing on the first two, we find that gravity is always attractive while the electromagnetic interaction can be either attractive or repulsive. For both of these interactions, we may define a force field in the following way:
A force field is a region in space produced by a source such that a test object placed in its vicinity will either be attracted or repelled to the source.
For example, in the case of Earth's gravity, we'd think of the Earth as the source; any test object placed in its vicinity will be attracted to it. Other types of force fields include electric fields, in which an electric force acts on all objects that have an electric charge, and magnetic fields, in which a magnetic force acts on all objects that have magnetic susceptibility —the property that causes them to be attracted to or repelled by a magnet. Now, barring the exception of like charges repelling each other, we find that force fields pull the test objects towards them despite not being in direct contact with them. That is, force fields produce long-range forces. This allows us to define a pulling force as follows:
A pulling force is a force in which an object moves towards the source of the interaction, either through direct contact or through the effect of a long-range force field.
To end this section, note that both pushing and pulling contact forces can be at work on the same object, as in the image below:
Pushing and pulling forces working together, public domain
Pulling Force Examples
Think of a pulling force as the force responsible for moving an object from a state of rest toward the source of the force. The object moves away from the surface of applied force. The time it takes to move the object depends on the reaction force exerted by the object.
Opening a door, plucking a guitar string, drawing a bucket of water from a well, and pulling a curtain are all examples of contact pulling forces.
The direction of a pulling force is the opposite of a push force.
We now have a good understanding of the way contact pulling forces work, so let's take a closer look at the magnetic force as an example of a long-range pulling force.
Magnet Pull Force
Think of the basics of how a magnet works. Magnets are capable of producing magnetic fields, attracting unlike poles and repelling like poles. A magnet's pull force is the force required to pull that magnet straight free vertically from a plate made out of any ferromagnetic material. It is a reliable method of measuring the limit of a magnet's holding power. Sellers and manufacturers that list the pull force of a magnet must perform this type of test to determine the strength before they can advertise the number. To get the most accurate reading of the pull force, the test must be done in three different ways, each assuming that the force used to pull the magnet is applied perpendicular to a flat surface:
1. Through the pull force test mentioned above.
2. By placing magnets between two steel plates.
3. By finding the amount of force needed to dislodge a magnet from an identical magnet.
Three pull force test methods for magnet strength StudySmarter Originals
Let us now examine how to measure the pulling force of gravity as another case of a long-range pulling force.
A Measure of the Pulling Force of Gravity
In fundamental terms, we know that weight measures the force of gravity pulling on an object. Weight is another word for the force of gravity near the surface of a planet. The SI unit for weight is the newton.
Weight is the force acting on an object due to gravity near the surface of a planet.
Weight should not be confused with mass. Keep in mind that mass has units of kg but since weight is a force it has units of N.
Weight is the force exerted on a body by gravity.
\[F_{\text{g}} = mg.\]
Numerically, we know that \(g\) is the acceleration due to gravity. Near Earth's surface, it has a value of \(9.8 \,\mathrm{m} / \mathrm{s}^2\). We can derive this value by solving for the acceleration in Newton's second law,
\[F = ma,\]
where the net force is given by Newton's law of universal gravitation:
\[F = G \frac{Mm}{r^2}.\]
Using \(g\) to denote the acceleration and substituting the second equation in the first, we get
\[g = G \frac{M}{r^2}.\]
Near Earth's surface, we can use the value of Earth's radius for \(r\) and the value of its mass for \(M\). However, this leaves \(G\), the gravitational constant, as an unknown without which we cannot justify our measure for the pulling force of gravity. Nowadays, we attribute the first empirical derivation of the value of \(G\) to Henry Cavendish.
The Cavendish Experiment
Henry Cavendish performed a classical experiment that first determined the value of Newton's constant \(G\), and was able to measure the pulling force of gravity. He determined the density of the Earth by using a torsion balance device to measure the weak gravitational force between lead balls. When the lead balls were attracted together, the bar turned to overcome torque resistance from the wire equal to the gravitational force between the balls. This is because the resistance is a function of the angle turned and the torsion coefficient of the wire. At some angle, the torque equals the gravitational force. In Cavendish's published paper on the experiment, he gave the value for the density and mass of the Earth but never mentioned the value for \(G\). It wasn't until other scientists repeated the experiment that they arrived at the modern value for \(G\). However, the value for \(G\) implied from Cavendish's experiment was very accurate and within 1% of present-day measurements.
The torsion balance allows for a measure of the pulling force of gravity public domain
Pulling Force Calculations
Let's finish this explanation by considering some examples involving pulling forces.
Remember that Newton's first law of motion or law of inertia says an object in a state of rest continues to be in a state of rest or moves with uniform velocity until an external unbalanced force acts on it. Let's review this law with a worked example:
Problem:
Some children ride the school bus on the way home from school when, suddenly, the school bus comes to a stop. All of the students' backpacks and lunchboxes on the floor start to slide forward. What do you think causes them to do that?
Solution:
The lunch boxes and backpacks on the floor continue their state of motion, maintaining their velocity (if friction is small enough to be ignored), as the velocity of the bus decreases. Newton's first law tells us that if no net force is acting on an object at rest, the object remains at rest; or if the object is moving, it continues moving with a constant speed in a straight line. In this case, there is no pulling force preventing the lunchboxes and backpacks from sliding forward.
Newton's second law says that acceleration produced in an object is directly proportional to the force acting on it and inversely proportional to the mass of the object. If a net force is exerted on an object the velocity of the object will change because a net force exerted on an object may make its velocity increase. Or, if the net force is in the opposite direction of the motion, the force will reduce the object's velocity.
Let's take a look at an example of using Newton's second law to solve a problem:
Problem: Force to stop a vehicle
A vehicle is driving on the highway, but it needs to come to a complete stop at the traffic light. What average net force is required to bring a \(1500\, \mathrm{kg}\) vehicle to rest from a speed of \(100 \, \mathrm{km/h}\) per hour within a distance of \(55 \,\mathrm{m}\)?
Average net force to stop a vehicle in acceleration StudySmarter Originals
Approach:
We can use Newton's second law to determine the force since we know the mass and acceleration of the vehicle. We have the mass but will need to calculate the acceleration \(a\). We assume the acceleration is constant so we can use the kinematic equations.
Solution:
We assume the motion is along the \(+x\)-axis. We are given the initial velocity \(v_0 = 100 \, \mathrm{km}/\mathrm{h} = 28 \, \mathrm{m}/\mathrm{s}\), the final velocity \(v = 0 \,\mathrm{m}/\mathrm{s}\) , and the distance traveled \(x - x_0 = 55\, \mathrm{m}\). Since the acceleration is the unknown quantity we're looking for, we can use the time-independent kinematic equation,
\[v^2 = v_0^2 + 2a(x-x_0)\]
so that
\[\begin{align} a &= \frac{v^2 - v^2_0}{2(x-x_0)} \\ &= \frac{(0 \,\mathrm{m}/\mathrm{s})^2 - (28 \, \mathrm{m}/\mathrm{s})^2}{2(55 \,\mathrm{m})} \\ &= -7.1 \,\mathrm{m}/\mathrm{s}^2. \end{align}\]
Then, the net force required is
\[\begin{align} F_{\text{net}} &= ma \\ &= (1500\, \mathrm{kg})(-7.1 \,\mathrm{m}/\mathrm{s}^2) \\ &= 1.1 \times 10^4 \,\mathrm{N}.\end{align}\]
The force must be exerted in the opposite direction of the initial velocity which is what the negative sign means. Note also, that the net force responsible for pulling the cart to a stop is the force of friction.
Pulling Forces - Key takeaways
- A pushing force is a force that aligns with the direction of the object's resulting state of motion.
- A pulling force is a force in which an object moves towards the source of the interaction, either through direct contact or through the effect of a long-range force field.
- Magnets are capable of producing magnetic fields, attracting unlike poles, and repelling like poles.
- A magnet's pull force is the force required to pull that magnet straight free vertically from a plate made out of any ferromagnetic material.
- Near Earth's surface, the weight equation gives a measure of the pulling force of gravity.
- We attribute to Henry Cavendish the first accurate measurement of the gravitational constant, \(G\), without which we wouldn't be able to derive the acceleration due to gravity.
References
- https://publicdomainvectors.org/en/free-clipart/Boys-carrying-crate/39172.html
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