Average and Instantaneous Power Example

Summary

In this video, students work through a physics problem involving a pumpkin dropped from a second-story window. The focus is on calculating the power delivered by the force of gravity at different stages of the pumpkin's fall. The script covers the use of formulas for average and instantaneous power, explaining concepts like displacement, velocity, and acceleration. The problem is broken into three parts: average power over the entire fall, instantaneous power just after the pumpkin is dropped, and instantaneous power right before it hits the ground. The students demonstrate various methods to solve the problem, including using velocity and force equations.

Takeaways

• 😀 Power is defined as the rate at which work is done or energy is transferred.
• 😀 The problem involves calculating the power delivered to a pumpkin dropped from a second-story window in three different contexts: average power, initial instantaneous power, and final instantaneous power.
• 😀 Part A requires calculating **average power** over the entire fall of the pumpkin, using the formula: Power = Work / Time.
• 😀 Work done by gravity is calculated as the force of gravity multiplied by displacement, and the force of gravity is mass × acceleration due to gravity.
• 😀 The **displacement** of the pumpkin is -8.91 meters, indicating a fall, and the force of gravity acts downwards.
• 😀 **Average velocity** is used in the power formula for Part A, and the result for average power is found to be 553 watts.
• 😀 In **Part B**, right after the pumpkin is dropped, the initial velocity is zero, so the instantaneous power is zero.
• 😀 **Instantaneous power** at a specific point in time can be calculated using the formula: Power = Force × Velocity × Cos(θ).
• 😀 For **Part C**, the velocity of the pumpkin right before it hits the ground is calculated using the kinematic equation: v_final = √(2 × g × d), which results in 13.22 m/s.
• 😀 The instantaneous power just before impact is 1110 watts, or approximately 1.48 horsepower, showing the increased power as the pumpkin gains speed during its fall.

Q & A

What is the main objective of the problem discussed in the script?

The main objective is to calculate the power delivered by the force of gravity to a pumpkin dropped from a second-story window, addressing average power and instantaneous power at different points during its fall.

How is power delivered by the force of gravity calculated in Part A?

In Part A, power is calculated using the formula: Power = Work / Change in time. The work done by gravity is calculated using the equation: Work = Force of gravity × Displacement × cos(θ). After finding the displacement and using the known mass of the pumpkin, the change in time is calculated, and the power is found to be 553 watts.

What was the mass of the pumpkin used in the problem?

The mass of the pumpkin is 8.53 kilograms.

What is the displacement in the Y direction when the pumpkin is dropped?

The displacement in the Y direction is -8.91 meters, indicating the pumpkin falls downward.

How do you determine the change in time for the pumpkin's fall?

The change in time is determined using the uniformly accelerated motion equation, which relates displacement, initial velocity, and acceleration. By substituting the known values, the change in time is calculated to be approximately 1.35 seconds.

Why is the initial velocity of the pumpkin zero in Part B?

The initial velocity is zero because the pumpkin is dropped from rest, meaning it has no initial velocity when it begins to fall.

What is the instantaneous power right after the pumpkin is dropped?

The instantaneous power right after the pumpkin is dropped is zero because the initial velocity is zero, and power is calculated using the equation Power = Force × Velocity × cos(θ), where velocity is zero at this moment.

How do you calculate the final velocity of the pumpkin just before it hits the ground?

The final velocity is calculated using the uniformly accelerated motion equation: v_final^2 = v_initial^2 + 2a × displacement. Substituting the values gives the final velocity in the Y direction as approximately -13.22 meters per second.

What is the instantaneous power right before the pumpkin strikes the ground?

The instantaneous power right before the pumpkin strikes the ground is 1110 watts. This is calculated using the force of gravity, the final velocity, and the cosine of the angle between the force and displacement.

How can the power be converted to horsepower?

The power in watts (1110 watts) is converted to horsepower by multiplying by the conversion factor 1 horsepower = 746 watts. This gives approximately 1.48 horsepower.