Physics 15 Torque (9 of 27) Alternative Method 1 & 2: Example Torque=?

Michel van Biezen
17 Jan 201604:00
EducationalLearning
32 Likes 10 Comments

TLDRThe video script outlines a method for calculating the net torque acting on a beam, assuming the mass of the beam is negligible. It presents a scenario with three forces (F1, F2, F3) applied at different distances from a pivot point A along the beam. The forces are applied at angles of 30°, 45°, and 10° respectively, with magnitudes of 50, 40, and 60 Newtons. The calculation involves multiplying each force by its respective distance from the pivot and cosine of the angle, then summing these products to find the net torque. The process simplifies to 50N * cos(30°) * 3m - 40N * cos(45°) * 5m + 60N * cos(10°) * 10m, which results in a net torque of 579 Newton meters, indicating a counterclockwise direction. The video emphasizes the utility of this method, especially when it's easier to determine the perpendicular distance from the force's line of action to the pivot point, and encourages viewers to choose the method that best suits their needs.

Takeaways
  • 📐 The example involves calculating the net torque on a beam with three forces acting on it, considering the distances from the pivot point and the angles of the forces.
  • 🚫 The mass of the beam is considered insignificant, so it can be ignored in the torque calculation.
  • ⚙️ The net torque is calculated by summing the individual torques caused by each force, taking into account their direction and magnitude.
  • 🔵 The first force (F1) causes a counterclockwise motion, which is considered a positive torque, calculated as F1 * distance * cos(30°).
  • 🔴 The second force (F2) results in a clockwise motion, indicating a negative torque, calculated as -F2 * distance * cos(45°).
  • 🟢 The third force (F3) also causes a counterclockwise motion, which is a positive torque, calculated as F3 * distance * cos(10°).
  • 🔢 The magnitudes of the forces are given as F1 = 50 Newtons, F2 = 40 Newtons, and F3 = 60 Newtons.
  • 📏 The distances from the forces to the pivot point are 3 m for F1, 5 m for F2, and 10 m for F3.
  • 🧮 The final calculation of the net torque is simplified by substituting the values for the forces and their respective distances and angles.
  • 📊 The net torque is found to be 579 Newton meters, which indicates a counterclockwise direction due to its positive value.
  • 🛠️ Two methods for finding torque are discussed: one using the perpendicular distance and the other using the line of action of the force to the pivot point.
  • ✅ The choice of method depends on the user's preference and which one is more convenient for the specific problem at hand.
Q & A

  • What is the total length of the beam in the given example?

    -The total length of the beam is 10 meters.

  • What is the distance from point A to where Force One is acting?

    -The distance from point A to where Force One is acting is 3 meters.

  • How is the torque caused by the first force described in terms of direction?

    -The first force causes a counterclockwise motion, which is described as a positive torque.

  • What is the formula used to calculate the torque caused by the first force?

    -The formula used is F1 * b1 * cos(30°), where F1 is the magnitude of the force, b1 is the distance from the force to the pivot point, and cos(30°) is the cosine of the angle between the vertical and the force.

  • What is the angle used for the cosine calculation of the second force's torque?

    -The angle used for the cosine calculation of the second force's torque is 45°.

  • Why is the torque caused by the second force considered negative?

    -The torque caused by the second force is considered negative because its vertical component would result in a clockwise motion.

  • What is the total net torque acting on the beam, according to the final calculation?

    -The total net torque acting on the beam is 579 Newton meters, which is a positive quantity indicating a counterclockwise direction.

  • What does the positive value of the net torque indicate about the direction of rotation?

    -A positive value of the net torque indicates that the rotation would be in a counterclockwise direction.

  • Why can the mass of the beam be ignored in this calculation?

    -The mass of the beam can be ignored because it is considered insignificant in the context of the problem, allowing for a simplification of the calculation.

  • What are the magnitudes of the three forces acting on the beam as given in the example?

    -The magnitudes of the three forces are 50 Newtons for Force 1, 40 Newtons for Force 2, and 60 Newtons for Force 3.

  • How does one find the net torque using the method described in the script?

    -The net torque is found by summing the individual torques caused by each force, taking into account their directions and the perpendicular distances to the pivot point.

  • What are the cosine values used for the forces in the final calculation?

    -The cosine values used are cos(30°) for Force 1, cos(45°) for Force 2, and cos(10°) for Force 3.

  • Why might one choose to use this method over finding the perpendicular distance to the line of action of the force?

    -One might choose to use this method when it is easier to determine the angle between the force and the vertical, rather than the perpendicular distance to the pivot point.

Outlines
00:00
🔍 Calculating Torque with Beam and Forces

This paragraph introduces a method for calculating the net torque on a beam with three forces acting on it. The beam is 10 meters long with distances of 3 meters, 5 meters, and 10 meters marked from a pivot point A. The forces are F1 (50 Newtons), F2 (40 Newtons), and F3 (60 Newtons), with F1 and F3 causing counterclockwise motion and F2 causing clockwise motion. The torque for each force is calculated by multiplying the force's magnitude by the distance to the pivot point and the cosine of the angle between the force and the vertical. The angles used are 30° for F1, 45° for F2, and 10° for F3. The final net torque is calculated after substituting the values, resulting in a positive 579 Newton meters, indicating a counterclockwise direction.

Mindmap
Keywords
💡Torque
Torque is the rotational equivalent of linear force and represents the turning or twisting effect of a force about an axis. In the video, torque is central to understanding how forces acting on a beam result in rotation around a pivot point. It is calculated as the product of the force magnitude, the distance from the pivot point to the line of action of the force, and the cosine of the angle between the force and the line perpendicular to the beam at the pivot point.
💡Beam
A beam is a horizontal or sloping structural element that primarily resists loads applied to it axially and by bending. In the context of the video, the beam is the object upon which forces are acting, and the calculation of torque is performed to determine the net effect of these forces on the beam's rotation.
💡Force
Force is a physical quantity that represents the interaction between objects and can cause a change in the motion of an object. In the video, different forces (F1, F2, F3) are applied at various distances from the pivot point, and their effects are analyzed to find the net torque acting on the beam.
💡Distance
Distance refers to the length of the space between two points. In the video, the distances from the point of application of each force to the pivot point (3 m, 5 m, and 10 m) are crucial in calculating the torque each force exerts on the beam.
💡Pivot Point
The pivot point is the point around which an object rotates or twists. In the video, the pivot point (point A) is the reference point from which distances to the forces are measured, and it is the center of rotation for the beam when torque is applied.
💡Cosine
The cosine function relates the angle of a right triangle to the ratio of the adjacent side over the hypotenuse. In the video, cosine is used to find the horizontal component of the force, which is necessary for calculating the torque. The cosine of the angles (30°, 45°, and 10°) is used in conjunction with the force magnitudes and distances to calculate the torque.
💡Counterclockwise
Counterclockwise refers to the direction of rotation that is opposite to the direction of the hands of a clock. In the video, a positive torque results in a counterclockwise rotation of the beam, which is indicated by the sign (positive or negative) when calculating the net torque.
💡Net Torque
Net torque is the vector sum of all the torques acting on an object. It determines the resulting rotational motion of the object. In the video, the net torque is calculated by summing the individual torques caused by the three forces acting on the beam, which dictates the overall rotation of the beam around the pivot point.
💡Newtons
Newtons (N) is the SI unit of force. It quantifies the magnitude of force acting on an object. In the video, the forces F1, F2, and F3 are given in Newtons, and these values are used to calculate the torque each force exerts on the beam.
💡Angles
Angles are measurements of rotation or the space between two intersecting lines or planes. In the video, specific angles (30°, 45°, and 10°) are provided to describe the direction of the forces relative to the vertical. These angles are essential for determining the cosine values used in the torque calculations.
💡Sum of the Torques
The sum of the torques is the total effect of all torques acting on a system. It is a principle used in the video to find the net torque acting on the beam, which is the algebraic sum of the individual torques caused by each force.
💡Direction of Rotation
The direction of rotation indicates whether an object rotates clockwise or counterclockwise. In the video, the direction is determined by the sign of the torque (positive for counterclockwise, negative for clockwise), which is crucial for understanding the final rotation of the beam.
Highlights

Different method of finding torque about a point demonstrated

Example involves a beam with three forces acting on it

Distances from point A to forces are 3m, 5m, and 5m

Total distance from point A to end of beam is 10m

Mass of beam is insignificant and can be ignored

Net torque is sum of torques about point A

First force (F1) causes positive (counterclockwise) torque

Second force (F2) causes negative (clockwise) torque

Third force (F3) causes positive (counterclockwise) torque

Torque calculation involves force magnitude, distance to pivot, and cosine of angle

Forces F1=50N, F2=40N, F3=60N at angles 30°, 45°, 10°

Plug in force and angle values to calculate net torque

Simplify the expression before calculating final answer

Net torque is 579 Nm, indicating counterclockwise rotation

Positive net torque means counterclockwise, negative means clockwise

Net torque about point A is also the net force on the beam at A

Two methods presented - choose the one that works best for you

This method is easier when finding the perpendicular distance is more straightforward

Demonstration shows step-by-step process for calculating torque using this method

Transcripts

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