Question

Early one October you go to a pumpkin patch to select your Halloween pumpkin. You lift a 3.2-kg pumpkin to a height of 0.80 m to check it out. How much work do you do on the pumpkin when you lift it from the ground?

Short answer

The work done on the pumpkin is 25.09 Joules.

Step-by-step solution

Understanding the Problem

The problem is asking us to calculate the work done when lifting a pumpkin from the ground to a certain height. We know the weight of the pumpkin and the height to which it is lifted.

Identify Key Formula

The formula for calculating work done against gravity is given by: \[ W = F \times d \]where \( F \) is the force (weight of the pumpkin) and \( d \) is the height (distance) the pumpkin is lifted.

Calculate the Force

The force exerted by the pumpkin due to gravity can be calculated using:\[ F = m \times g \]where \( m = 3.2 \, \text{kg} \) is the mass of the pumpkin and \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.

Perform the Calculation for Force

Substitute the values:\[ F = 3.2 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 31.36 \, \text{N} \]This is the force exerted by the pumpkin's weight.

Calculate the Work Done

Now that we have the force, use the work formula:\[ W = 31.36 \, \text{N} \times 0.80 \, \text{m} \]Calculate the work done.

Perform the Calculation for Work

Substitute the values into the work formula:\[ W = 31.36 \, \text{N} \times 0.80 \, \text{m} = 25.088 \, \text{J} \]Thus, the work done on the pumpkin is about 25.09 Joules.

Key concepts

Calculation of Work

In physics, calculating work is important to understand how energy is transferred when an object is moved by a force over a distance. Work, denoted as "W", is the product of force "F" and the distance "d" over which the force is applied. The formula for work is given by: \[ W = F \times d \]This calculation tells us how much energy is being used in moving the object. When we lift something, like a pumpkin, against gravity, the force you exert is often equal to the weight of the object. This weight is calculated based on the object's mass and the gravitational pull, usually approximated by \(9.8\, \text{m/s}^2\) on Earth. This simple formula helps in understanding the relationships between force, distance, and work done. For any object, knowing how much energy is required to move it is crucial, especially in engineering and physics applications.

Force and Gravity

Force is a vector quantity that, in this context, refers to the push or pull applied to move an object. When you lift an object, like the pumpkin in our exercise, the force required is often a result of gravity acting on the object's mass. Gravity pulls objects towards the Earth, providing the force needed to calculate weight. This is done via the formula: \[ F = m \times g \]where "\( m \)" is the mass of the object and "\( g \)" is the acceleration due to gravity. For most calculations on Earth, \( g \approx 9.8\, \text{m/s}^2\).

• Mass (\(m\)) is measured in kilograms (kg).
• Gravity (\(g\)) is measured in meters per second squared (m/s\(^2\)).
• The force due to gravity (weight) is measured in newtons (N).
  

Understanding the effect of gravity is essential for calculations in physics, as it allows us to determine the necessary energy and force needed to move an object vertically.

Lifting Objects Physics

In the physics of lifting objects, several key principles come into play concerning energy and force. When you lift an object, you are working against the force of gravity. This requires the application of a force equal to the object's weight, plus additional force to accelerate the object upwards. The amount of work done in lifting the object is crucial for determining the energy expended. The work done is affected by:

• The weight of the object, determined by its mass and gravity.
• The height you lift it, which is the distance in the work formula.

In real-world applications, understanding these principles helps in efficiently planning activities like material handling in construction or carrying groceries. It is these basic principles that allow engineers and physicists to design better machinery and tools that help lift objects with less energy. By lifting something such as a pumpkin, you exert a force that is translated into energy expenditure, comprehending how energy, work, and force interplay is central to solving practical physics problems.