Problem 24 - Applied Physics

Question

A pallet is loaded with bags of cement; the total weight of \(875 \mathrm{~N}\) is lifted \(21.0 \mathrm{~m}\) vertically in \(11.0 \mathrm{~s}\). What power in kilowatts is required to lift the cement?

Step-by-Step Solution

Answer

The power required is approximately 1.67 kW.

Step 1: Understand the Problem

We need to find the power required to lift a pallet with cement bags vertically. The key parameters given are: the total weight of the pallet, the height it is lifted, and the time taken to lift it.

Step 2: Formula Identification

The power required can be calculated using the formula for power in terms of work and time: \( P = \frac{W}{t} \), where \( P \) is power, \( W \) is work done, and \( t \) is the time taken. First, we need to find the work done.

Step 3: Calculate Work Done

The work done is equal to the change in potential energy when lifting the mass, which can be calculated by \( W = F \cdot d \), where \( F \) is the force (weight of the pallet) and \( d \) is the distance. Here, \( F = 875 \) N and \( d = 21.0 \) m. So, \( W = 875 \times 21.0 \).

Step 4: Work Done Computation

Calculate the work done: \( W = 875 \times 21.0 = 18375 \) Joules.

Step 5: Calculate Power

Substitute the values into the power formula: \( P = \frac{W}{t} = \frac{18375}{11.0} \).

Step 6: Power Computation in Watts

Calculate the power in watts: \( P = \frac{18375}{11.0} = 1670.45 \) Watts.

Step 7: Convert Power to Kilowatts

Convert the power from watts to kilowatts by dividing by 1000: \( P = \frac{1670.45}{1000} = 1.67045 \) kW.

Key Concepts

Work Done

When we talk about "work done" in physics, we're referring to the amount of energy transferred when an object is moved by a force. The formula to calculate work done is fairly straightforward:

• Work done (\(W\)) = Force (\(F\)) × Distance (\(d\))

This formula tells us that the work done is the product of the force applied to an object and the distance over which that force is applied. In the exercise, the force is the weight of the pallet, which is 875 N, and the distance is 21.0 m. So we have:\[W = 875 \times 21.0 = 18375\text{ Joules}\]You'll notice that work done is measured in joules, a standard unit of energy. This calculation helps understand the energy needed to lift the cement-loaded pallet against gravity.

Potential Energy

Potential energy is a type of stored energy that depends on the position or arrangement of an object. For lifting scenarios, this energy is primarily gravitational potential energy.It represents the energy stored due to an object's height above the ground. The formula for calculating the gravitational potential energy is:

• Gravitational Potential Energy (\(PE\)) = Weight (\(F\)) × Height (\(h\))

This yields the same result as the work done when lifting an object vertically. For our problem, since we are lifting the pallet to a height of 21.0 m, the potential energy is:\[PE = 875 \times 21.0 = 18375\text{ Joules}\]It's vital to see how potential energy connects with work done because whenever an object gains height, it stores energy as potential energy.

Lifting Force

The lifting force is closely related to the concept of weight, which is a measure of the gravitational force on an object. Weight is calculated by multiplying mass (\(m\)) by the acceleration due to gravity (\(g\)), approximately 9.8 m/s² on Earth.In our exercise, however, the weight is given directly as 875 N. This means the lifting force required to move the pallet upwards is also 875 N, since it must counteract this gravitational force.This force ensures that the object moves to the desired height. It's key to remember:

• Lifting Force = Gravitational Force

By using the weight provided, you can directly calculate the work done and potential energy without needing to further convert or adjust for lifting scenarios.

Physics Problem-Solving

Solving physics problems involves understanding the connections between different concepts, like force, work, and energy. Each concept usually correlates to a specific formula that links it with measurable quantities.Here are a few steps to approach physics problem-solving effectively:

• Identify the Problem: Recognize what's being asked. Are you finding work, energy, or force?
• Know Your Formulas: Ensure you know the key formulas like \(W = F \cdot d\) or \(P = \frac{W}{t}\).
• Divide the Task: Break the problem into smaller, manageable parts. Solve each part in sequence.
• Check Units: Make sure your answer’s units are appropriate for the physical quantity asked.
• Re-evaluate: Always double-check calculations to ensure accuracy.

Approaching each problem with these steps can simplify complex situations and enhance your understanding of physics concepts. This strategy was used in the given exercise to find the power needed to lift the cement pallet.