Placing the Fulcrum on a Seesaw

Summary

In this engaging physics lesson, Mr. P and his students explore the concept of static equilibrium using a seesaw problem. The students model a system with two masses and a meterstick, aiming to find the position of the fulcrum that balances the system. Through a series of calculations and discussions on torques and forces, they determine that the fulcrum must be placed at the 45 cm mark. The lesson emphasizes the importance of understanding rotational equilibrium and illustrates how estimates and assumptions don't affect the final solution, reinforcing key physics principles in a hands-on, interactive manner.

Takeaways

• 😀 The problem involves balancing a seesaw with two kids using a movable fulcrum, which is modeled with a meterstick, masses, and a domino.
• 😀 The fulcrum's location is crucial for balancing the seesaw. The goal is to determine the exact point where it should be placed.
• 😀 The meterstick is uniform, with a mass of 93g and a center of mass at the 50 cm mark. The two masses (200g and 100g) are placed at different positions (20 cm and 90 cm).
• 😀 The balance is achieved when the torques from all forces acting on the seesaw are equal and opposite, meaning the net torque is zero.
• 😀 The forces acting on the meterstick include the weight of the masses and the weight of the meterstick itself, all of which cause different torques.
• 😀 The system needs to be in static equilibrium, meaning both translational and rotational equilibrium must be satisfied.
• 😀 The axis of rotation is chosen to be at the left end of the meterstick, simplifying the calculations by making the torque from the normal force positive.
• 😀 The torque equation involves calculating the torque from each force (gravitational forces on masses and the meterstick) and setting the sum of torques to zero.
• 😀 A simplified approach removes the need to calculate the normal force directly, focusing instead on finding the location of the fulcrum based on the net torque.
• 😀 After solving the equation, the fulcrum's location is determined to be at the 45 cm mark, which balances the system.
• 😀 The important point is that the estimated location of the fulcrum does not affect the final solution, as the net torque equation will still work regardless of the initial estimate.

Q & A

What is the main physics principle being applied in this problem?

The main principle being applied is static equilibrium, specifically balancing forces and torques to determine the position of the fulcrum on the seesaw (meterstick).

Why does the fulcrum need to be placed at a specific location?

The fulcrum must be placed at a location where the torques created by the weights of the masses and the meterstick balance each other, resulting in rotational equilibrium.

What role does the force normal play in this problem?

The force normal acts upward at the fulcrum and is crucial for balancing the downward forces of gravity. It ensures that the meterstick does not rotate or accelerate vertically.

Why is it important to consider torques rather than just forces?

Since the meterstick is rotating, it is necessary to consider torques (which are a function of force and distance from the pivot point) to determine the balance point, not just the forces acting vertically.

How do you calculate the location of the fulcrum?

The location of the fulcrum is calculated by setting the sum of the torques about the fulcrum equal to zero, using the formula that considers the positions of all forces (masses and meterstick) and their respective distances from the fulcrum.

Why does the acceleration due to gravity cancel out in the final calculation?

The acceleration due to gravity cancels out because it is a common factor in all the forces acting on the system, making it irrelevant to the location of the fulcrum in terms of mass distribution and torque.

What would happen if the estimated location of the fulcrum were incorrect?

Even if the estimated location of the fulcrum is wrong, the physics will still work. The final calculation for the force normal will determine the correct position of the fulcrum regardless of the initial guess.

What is the significance of using a free-body diagram in this problem?

A free-body diagram is essential to visualize all the forces acting on the meterstick, allowing for the accurate application of Newton's laws of motion (both translational and rotational) to solve for the fulcrum location.

Why is the assumption of static equilibrium important in this problem?

The assumption of static equilibrium is important because it ensures that both the forces and torques acting on the meterstick are balanced, meaning there is no motion or rotation occurring.

What alternative method could have been used to solve the problem?

An alternative method would be to set the axis of rotation at the location of the force normal. This would simplify the torque equation by eliminating the torque due to the force normal but complicating the other torques. The solution could still be reached, though.