How the Force of Tension on a Pulley Changes with Acceleration

Summary

In this lesson, Mr. P guides students through the process of understanding how the force of tension in a string varies with the acceleration of a pulley system. By measuring the force of tension and considering free body diagrams, the class explores how tension changes when the pulley begins to accelerate. The discussion includes solving for the force of tension before and after the pulley is released, using principles of torque and acceleration. The lesson highlights the relationship between tension, gravity, and acceleration in a rotating system.

Takeaways

• 😀 The rotational inertia of the demonstrator was determined by measuring the force of tension on the hanging mass, which equals the force of tension acting on the pulley.
• 😀 The force of tension decreases when the pulley is released, and the hanging mass begins to accelerate downwards.
• 😀 Free body diagrams help explain the forces acting on the system, including the force of gravity on both the pulley and hanging mass.
• 😀 The tension force acts in opposite directions on both ends of the string: downward on the pulley and upward on the hanging mass.
• 😀 The system’s force of gravity and the normal force on the pulley are balanced, while the hanging mass has both gravity and the force of tension acting on it.
• 😀 The rotational direction for torque is counterclockwise or out of the board, considered the positive direction.
• 😀 Before releasing the pulley, the system is at rest, meaning the force of tension equals the gravitational force acting on the hanging mass.
• 😀 The hanging mass is 0.103 kg, which includes the mass of the force sensor, and the force of gravity is calculated as 1.01 newtons.
• 😀 After the pulley is released, the force of tension is calculated by factoring in the angular acceleration of the pulley and the acceleration of the hanging mass.
• 😀 The predicted and measured force of tension while the system accelerates is very close, with the measured force being 0.955 newtons and the predicted force being 0.948 newtons.
• 😀 The force of tension in the string decreases once the system starts to accelerate, influenced by the angular acceleration of the pulley.

Q & A

What is the key concept demonstrated in this video script?

The key concept is the relationship between the force of tension in the string and the acceleration of the hanging mass, or the angular acceleration of the pulley.

Why does the measured force of tension decrease after the pulley is released?

The force of tension decreases because, as the pulley is released, the system starts to accelerate. The force of tension is influenced by the acceleration of the hanging mass, which leads to a reduction in the tension once the system begins to move.

What role does the free body diagram play in understanding the forces in this system?

The free body diagram helps to visualize the forces acting on the pulley and hanging mass, which are necessary for applying Newton's laws and calculating the force of tension and other forces involved in the system.

How do the forces on the pulley and hanging mass compare before the system is released?

Before the system is released, the forces are in equilibrium. The force of tension on the pulley equals the force of gravity acting on the hanging mass, meaning there is no movement, and the acceleration in the y-direction is zero.

What is the mass of the hanging object in this experiment?

The mass of the hanging object, including the mass of the force sensor, is 0.103 kilograms.

What equation is used to calculate the force of tension before the pulley is released?

The equation used is the force balance in the y-direction: Force of tension - Force of gravity = 0, since the system is at rest, meaning the acceleration in the y-direction is zero.

How do you calculate the force of tension after the pulley is released?

After the pulley is released, the force of tension is calculated by taking into account the acceleration of the hanging mass. The equation is: Force of tension = mass × (gravity - radius × angular acceleration).

What is the angular acceleration of the pulley in this experiment?

The angular acceleration of the pulley is 29.910 radians per second squared.

How does the radius of the pulley factor into the calculation of the force of tension?

The radius of the pulley is used to relate the angular acceleration of the pulley to the linear acceleration of the hanging mass. The radius is multiplied by the angular acceleration to determine the tangential acceleration, which affects the force of tension.

How accurate is the measured force of tension compared to the predicted value?

The measured average force of tension while the system is accelerating is 0.955 newtons, which is very close to the predicted value of 0.948 newtons, indicating a good match between the measurement and calculation.