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🍏principles of physics i review

T=mg

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The equation t=mg represents the relationship between tension (t) in a rope or string and the weight (mg) of an object connected to it. In this equation, 't' is the tension force acting on an object while 'm' is its mass and 'g' is the acceleration due to gravity. This relationship is crucial for understanding how forces are transmitted through connected objects, especially in scenarios involving pulleys or hanging masses.

5 Must Know Facts For Your Next Test

  1. In a static situation where an object is at rest and connected by a rope, the tension force equals the weight of the object, so t=mg holds true.
  2. If multiple objects are connected in a series, such as in a pulley system, tension will be the same throughout the rope if we neglect friction and mass of the rope.
  3. In an accelerating system, like an object being pulled upward with acceleration 'a', the tension can be calculated as t=m(g+a).
  4. The unit for tension is Newtons (N), just like weight, since both are forces resulting from mass and acceleration.
  5. When dealing with angles, such as in an inclined plane scenario, you need to break down forces into components to find effective tension using trigonometric functions.

Review Questions

  • How does the equation t=mg apply to a scenario involving two masses connected by a pulley?
    • In a scenario with two masses connected by a pulley, each mass experiences gravitational force represented by mg. The tension in the rope connecting them will equal mg for each mass if they are at rest. If one mass is heavier and causes acceleration, then tension can change based on both weights and any applied forces. Understanding this relationship helps predict motion and calculate forces in connected systems.
  • What factors influence the tension in a rope when multiple objects are involved in a dynamic system?
    • In a dynamic system with multiple objects, factors influencing tension include the masses of the objects, their acceleration, and any external forces applied. For example, if one object is being accelerated upwards or downwards, that acceleration affects the tension calculated using t=m(g+a) or t=m(g-a). Additionally, friction in pulleys or differences in height can also affect tension throughout the system.
  • Evaluate how variations in mass and acceleration affect the application of t=mg in complex systems involving connected objects.
    • In complex systems involving connected objects, variations in mass and acceleration significantly impact how t=mg is applied. When different masses are involved, such as in a multi-pulley system or when one object has additional forces acting on it (like friction), calculating tension becomes more complicated. Analyzing these variables allows for predictions about movement and stability within the system. Understanding these interactions can lead to better designs in mechanical systems that rely on connections between objects.