Torque on a Bolt | Physics with Professor Matt Anderson | M12-10

Physics with Professor Matt Anderson
1 Nov 202103:01
EducationalLearning
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TLDRIn this educational transcript, Professor Anderson introduces a torque problem involving the removal of a bolt. The scenario presents a wrench applied to the bolt at an angle of 105 degrees due to geometric constraints, rather than the ideal perpendicular approach. Given the bolt requires a torque of 33 Newton meters to loosen, and with a wrench length of 29 centimeters (0.29 meters), the problem is to determine the force (F) needed to apply on the wrench. The solution is derived using the torque formula, which equates torque to the product of the force, the lever arm, and the sine of the angle (phi). By substituting the given values into the formula ( F = \( \frac{\text{Torque}}{r \cdot \sin(\phi)} \) ), the calculated force required is 117.8 Newtons. This concise explanation provides a clear understanding of how to calculate the force needed in such a practical situation, encouraging students to apply their knowledge of physics to real-world problems.

Takeaways
  • ๐Ÿ”ฉ The problem involves calculating the force required to loosen a bolt using a wrench.
  • ๐Ÿ“ The wrench is not pulled at a right angle but at an angle of 105 degrees to the bolt.
  • ๐Ÿ› ๏ธ Torque is the key concept, defined as the force times the lever arm or the perpendicular component of the force times the radius.
  • ๐Ÿ“ The wrench length (lever arm) is given as 29 centimeters or 0.29 meters.
  • ๐Ÿ”ข The torque required to loosen the bolt is specified as 33 Newton meters.
  • ๐Ÿ“ The angle at which the wrench is pulled is 105 degrees, which is greater than 90 degrees.
  • โš™๏ธ The formula to calculate the force (f) is torque divided by the lever arm (r) times the sine of the angle (phi).
  • ๐Ÿงฎ By substituting the given values into the formula, the force required is calculated to be 117.8 Newtons.
  • ๐Ÿ” The calculation involves understanding the relationship between torque, force, and the angle of application.
  • ๐Ÿค” The problem emphasizes the importance of considering the angle when calculating the force needed to apply torque.
  • ๐Ÿ‘จโ€๐Ÿซ Professor Anderson encourages students to seek further clarification if the explanation is not clear, offering help in his office.
Q & A

  • What is the scenario described in the problem?

    -The scenario involves removing a bolt with a wrench, but the geometry requires pulling the wrench at an angle rather than directly perpendicular.

  • What angle is the wrench being pulled at, and how does it affect the torque calculation?

    -The wrench is pulled at a 105-degree angle, which requires calculating the perpendicular component of the force to determine the torque.

  • What formula is used to calculate torque in this scenario?

    -The formula used is torque = r * F * sin(ฯ•), where r is the lever arm, F is the force applied, and ฯ• is the angle.

  • What is the required torque value needed to loosen the bolt?

    -The required torque value is 33 Newton meters.

  • What is the length of the wrench used in the problem?

    -The wrench is 29 centimeters long, which equals 0.29 meters.

  • What is the relationship between torque, lever arm, and force in this scenario?

    -The torque is directly proportional to the product of the lever arm length and the perpendicular component of the force applied.

  • How is the force needed to loosen the bolt calculated?

    -The force needed is calculated by rearranging the torque formula to F = torque / (r * sin(ฯ•)).

  • What is the value of the calculated force needed to loosen the bolt?

    -The calculated force needed is 117.8 Newtons.

  • Why is the angle of the wrench important in the calculation?

    -The angle determines the perpendicular component of the force applied to the lever arm, which directly affects the torque.

  • What should a student do if the explanation is unclear?

    -The student is encouraged to visit the professor's office for clarification.

Outlines
00:00
๐Ÿ”ง Torque Calculation for Loosening a Bolt

Professor Anderson introduces a physics problem involving torque, specifically the force required to loosen a bolt using a wrench. The bolt is not accessible at a right angle, so the wrench must be pulled at an angle of 105 degrees. Given a torque of 33 Newton meters needed to break the bolt free and a wrench length of 29 centimeters (0.29 meters), the problem is to find the force (F) necessary to apply to the wrench. The formula for torque is discussed, which is the product of the force, the lever arm, and the sine of the angle between them (r * F * sin(phi)). Using the provided values, the force required is calculated to be 117.8 Newtons. The professor encourages students to approach him if they have any questions.

Mindmap
Keywords
๐Ÿ’กTorque
Torque is a measure of the force that can cause an object to rotate about an axis. It is defined as the product of the force vector and the lever arm vector, which is the perpendicular distance from the axis of rotation to the line of action of the force. In the video, torque is the key concept for understanding how much force is needed to loosen the bolt, with the formula being torque equals force times the lever arm.
๐Ÿ’กBolt
A bolt is a cylindrical fastener with an external screw thread, used to hold two parts together. In the context of the video, the bolt is the object that needs to be loosened using a wrench, and the problem revolves around calculating the force required to achieve this.
๐Ÿ’กWrench
A wrench is a tool used to provide grip and mechanical advantage when applying torque to turn objects, such as nuts and bolts. In the video, the wrench is the tool used to apply the force necessary to loosen the bolt, with the length of the wrench being a factor in the calculation.
๐Ÿ’กAngle
In the context of the video, the angle refers to the angle at which the wrench is applied to the bolt. It is given as 105 degrees, which is greater than 90 degrees, indicating that the force is not being applied directly opposite the bolt's axis of rotation.
๐Ÿ’กNewton Meters
Newton meters is a unit of measurement for torque. It represents the amount of force required to cause an object to rotate. In the video, the bolt comes loose if the torque on the bolt is equal to 33 newton meters, which is the target torque value to be achieved.
๐Ÿ’กLever Arm
The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. It is a critical component in the calculation of torque. In the video, the wrench length of 0.29 meters serves as the lever arm in the torque equation.
๐Ÿ’กForce
Force is a physical quantity that represents the interaction causing a change in the motion of an object. In the video, the force that needs to be applied to the wrench to loosen the bolt is the unknown variable that the calculation aims to find, with the final result being 117.8 newtons.
๐Ÿ’กPerpendicular Component
The perpendicular component of a force is the part of the force that acts at a right angle to a given direction, in this case, the direction of the lever arm. It is used in the torque equation to calculate the effective force that contributes to rotation.
๐Ÿ’กPhi
In the context of the video, phi (ฯ†) represents the angle between the force vector and the lever arm. It is used in the formula for torque as torque equals the radius times the force times the sine of phi (r * f * sin(ฯ†)). The angle is given as 105 degrees.
๐Ÿ’กCalculation
Calculation refers to the process of computing a value or result from given information using mathematical methods. In the video, the calculation is used to determine the force (f) required to loosen the bolt by using the known values for torque, the lever arm, and the angle.
๐Ÿ’กSine
The sine function is a trigonometric function that in the context of the video, is used in the formula to calculate torque. It gives the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. The sine of the angle (105 degrees) is used to find the perpendicular component of the force.
Highlights

Professor Anderson introduces a torque problem involving removing a bolt.

The bolt is located in such a way that the wrench cannot be pulled at a right angle.

A wrench is used to apply force at an angle of 105 degrees to the bolt.

The bolt requires a torque of 33 Newton meters to break free.

The length of the wrench used is 29 centimeters or 0.29 meters.

The goal is to determine the force (F) needed to loosen the bolt.

Torque is defined as the product of force times the lever arm.

An alternative expression for torque is the radius times the perpendicular component of the force.

Torque can also be expressed as the radius times the force times the sine of the angle (r * f * sin(phi)).

The formula to solve for the force (F) is F = torque / (r * sin(phi)).

Substituting the given values into the formula yields a force of 117.8 Newtons.

The force of 117.8 Newtons is the amount needed to pull on the wrench to loosen the bolt.

Professor Anderson encourages students to seek clarification if the problem is not clear.

The problem demonstrates the application of torque in a practical scenario.

Understanding the relationship between torque, force, and angle is crucial for solving the problem.

The problem involves converting degrees to radians if using a calculator.

The use of the sine function in the torque formula accounts for the angle of application of the force.

The problem highlights the importance of geometry in the application of forces.

Professor Anderson's approach to the problem emphasizes a step-by-step method.

The problem-solving process is designed to be accessible and understandable to students.

Transcripts

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