# The force of tension | Forces and Newton's laws of motion | Physics | Khan Academy

TLDRThis transcript delves into the concept of tension, a force often misunderstood in physics. The instructor clarifies that tension is the force exerted by a rope or cable, and explains how it's transmitted through its fibers. The discussion addresses common misconceptions about tension, such as the rope pushing on an object, when in fact it's a pulling force. The solution to finding tension in various scenarios is explored using Newton's Second Law, highlighting the importance of considering the direction and magnitude of forces, and the assumption of a massless rope for simplicity in calculations.

###### Takeaways

- π Tension is the force exerted by a rope, string, or cable, and is transmitted through its fibers.
- π Tension problems can be demystified by understanding common misconceptions and treating tension like any other force.
- π― The force of tension is useful for transmitting force over a distance, as seen in physics problems involving boxes and ropes.
- βοΈ In physics problems, ropes are often assumed to be massless to simplify calculations, meaning the rope's mass is negligible compared to other masses in the system.
- π Tension is a pulling force, not a pushing force, and is represented by an arrow pointing in the direction of the pull.
- π Newton's Second Law (F = ma) is used to calculate tension, as there is no direct formula for tension like there is for gravity (F = mg).
- π€ΉββοΈ When multiple forces act on a system, such as multiple ropes pulling in different directions, the net force and acceleration must be considered.
- π To solve for tension with angled forces, trigonometry is used to find the horizontal component of the force.
- π The tension in a rope is assumed to be the same at all points if the rope is massless or its mass is insignificant.
- π« Be cautious not to draw acceleration as a force; it is the result of a force and should be represented differently.
- π In complex problems, include all relevant forces (even friction) and use Newton's Second Law to algebraically solve for the unknown tension.

###### Q & A

### What is tension in the context of physics?

-Tension is the force exerted by a rope, string, or cable, or any rope-like object, that transmits force over a distance when pulled or stretched.

### Why do students find problems involving the force of tension challenging?

-Students find tension problems challenging because they often involve misconceptions about the nature of tension and its direction, as well as the complexity of dealing with varying tensions along the length of the rope when it's not considered massless.

### How does the composition of a rope affect the transmission of force?

-Ropes are typically composed of fibers braided or wound together, which allows a force exerted at one end to be transmitted through the rope to the other end, pulling on the fibers and eventually exerting a force on an object like a box.

### What is the typical assumption made in physics problems regarding the mass of the rope?

-In physics problems, the rope is often assumed to be massless to simplify calculations. This means that the mass of the rope is negligible compared to other masses in the problem, and variations in tension due to the rope's weight are ignored.

### How is tension different from other forces like gravity?

-Tension is a pulling force transmitted through a rope or similar object, whereas gravity is a pushing force that acts on all masses due to the attraction of the Earth. Tension requires a rope or similar object to be present, while gravity acts universally.

### What is the formula used to calculate the force of gravity?

-The force of gravity is calculated using the formula mg, where m is the mass of the object and g is the acceleration due to gravity.

### How do you determine the direction of tension in a force diagram?

-In a force diagram, the direction of tension is depicted as pulling on the object. If the rope is pulling to the right, the tension is considered positive; if pulling to the left, it is considered negative.

### What is Newton's Second Law of Motion and how is it used to solve for tension?

-Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. It is used to solve for tension by setting the net force equal to the mass times the acceleration (F = ma) and solving for the tension force.

### How do additional forces, such as multiple ropes pulling in different directions, affect the calculation of tension?

-Additional forces from multiple ropes pulling in different directions require considering each force's component in the direction of interest. Forces pulling in the same direction as the desired acceleration increase the required tension, while forces pulling in the opposite direction decrease it, and forces at an angle must have their horizontal components considered.

### Why is it important to consider the rope's mass when calculating tension?

-Considering the rope's mass is important because if the rope has significant mass, the tension varies along its length, with greater tension near the force application and lesser tension at the load. Ignoring the rope's mass can lead to incorrect calculations of the force required to achieve a certain acceleration.

### What is the role of trigonometry in calculating the horizontal component of a tension force that is applied at an angle?

-Trigonometry is used to find the horizontal component (T_x) of a tension force (T) applied at an angle (ΞΈ) by using the cosine of the angle. The horizontal component is given by T_x = T * cos(ΞΈ), which is then used in the Newton's Second Law equation to solve for other forces or tensions in the system.

###### Outlines

##### π Understanding Tension in Physics

This paragraph introduces the concept of tension as a force exerted by a rope, string, or cable. The instructor aims to clarify misconceptions about tension and make students more comfortable with solving problems involving it. Tension is explained as a pulling force transmitted through the fibers of a rope, and its practical application is discussed, such as how it allows for the transmission of force over a distance. The instructor also addresses the common physics problem assumption of a massless rope, explaining that it simplifies calculations by neglecting variations in tension due to the rope's mass.

##### π Analyzing Tension with Newton's Second Law

The paragraph delves into how to solve for tension using Newton's Second Law. It emphasizes that tension is a pulling force, not a pushing force, and this must be reflected in diagrams. The process of solving for tension involves identifying the net force and acceleration, and applying the law to find the required tension to achieve a given acceleration. The paragraph also introduces a more complex scenario where multiple ropes exert tension in different directions, and explains how to account for additional forces in the calculations.

##### π Calculating Tension with Trigonometry

This paragraph further complicates the tension problem by introducing a force exerted at an angle. The instructor explains how to use trigonometry to find the horizontal component of this force and how to incorporate it into the Newton's Second Law equation. The explanation includes the use of cosine for the calculation of the horizontal component and the impact of additional forces on the required tension. The paragraph reinforces the idea that tension is transmitted equally throughout the rope when its mass is negligible or massless.

###### Mindmap

###### Keywords

##### π‘Tension

##### π‘Force

##### π‘Acceleration

##### π‘Newton's Second Law

##### π‘Mass

##### π‘Rope Composition

##### π‘Force Diagram

##### π‘Friction

##### π‘Components of Force

##### π‘Trigonometry

##### π‘Net Force

###### Highlights

Tension is the force exerted by a rope, string, or cable, or any rope-like object, and is transmitted through the rope.

Tension is useful because it allows the transmission of force over a large distance.

In physics problems, ropes are often assumed to be massless to simplify calculations, meaning the rope's mass is negligible compared to other masses in the problem.

Tension is a pulling force, not a pushing force, asη»³ε (ropes) can only pull on objects, not push.

To solve for tension, one must use Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

When drawing a force diagram, the force of tension should point in the direction of the pull, which is typically to the right if the rope is being pulled horizontally.

If additional forces are acting on the object, such as another tension force or friction, these must be included in the force diagram and calculations.

When multiple tension forces are involved, the total tension required to maintain a certain acceleration may change, as the individual tensions can either assist or oppose each other.

In more complex scenarios, such as when a tension force is applied at an angle, trigonometry is used to determine the horizontal component of the force for calculations.

The force of tension is uniform throughout the rope when the rope is considered massless or when its mass is insignificant compared to other masses in the system.

If the rope had significant mass, there would be a variation in tension along its length, with the tension decreasing from the point of application of the force.

In real-world applications, the assumption of a massless rope simplifies the problem and avoids the need to account for variations in tension due to the rope's mass.

The concept of tension is important in various practical situations, such as in the transportation of goods or in the design of structures where ropes or cables are used.

Misunderstanding tension can lead to errors in problem-solving, hence it's crucial to grasp the nature of tension as a pulling force and how it's transmitted through a rope.

When solving problems involving tension, it's essential to correctly identify and apply the signs to all forces in the force diagram to accurately calculate the tension.

The force of tension is a fundamental concept in mechanics and understanding it is key to solving a wide range of physics problems involving ropes or cables.

In summary, to find the tension in a system, one must apply Newton's Second Law, correctly interpret the direction of forces, and perform the necessary algebraic manipulations.

The force of tension is unique in that it can only pull and cannot push, which distinguishes it from other types of forces encountered in mechanics.

###### Transcripts

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