Problem 23 - Applied Physics

Question

A pallet weighing \(575 \mathrm{~N}\) is lifted a distance of \(20.0 \mathrm{~m}\) vertically in \(10.0 \mathrm{~s}\). What power is developed in kilowatts?

Step-by-Step Solution

Answer

The power developed is 1.15 kW.

Step 1: Calculate Work Done

Work (W) is calculated using the formula: \[ W = F \cdot d \]where F is the force (575 N) and d is the distance (20.0 m). Substitute the given values:\[ W = 575 \times 20.0 = 11500 \text{ J} \]So, the work done is 11500 Joules.

Step 2: Calculate Power in Watts

Power (P) can be calculated using the formula: \[ P = \frac{W}{t} \]where W is the work (11500 J) and t is the time (10.0 s). Substitute the values:\[ P = \frac{11500}{10.0} = 1150 \text{ W} \]So, the power developed is 1150 Watts.

Step 3: Convert Power to Kilowatts

To convert power from Watts to kilowatts, divide the power in Watts by 1000:\[ P = \frac{1150}{1000} = 1.15 \text{ kW} \]Therefore, the power developed in kilowatts is 1.15 kW.

Key Concepts

Work-Energy Principle

The work-energy principle is a crucial concept in physics, which states that the work done on an object is equal to the change in its kinetic energy. This principle helps us understand how energy is transferred or transformed when work is performed. In the context of the given exercise, lifting a pallet vertically involves doing work against gravitational force.

• The exerted force causes a change in the potential energy of the pallet.
• The formula to calculate work, which is the product of force and distance, plays a central role here.

This principle allows us to directly link the energy transfer (via work done) and the resultant energy changes, providing insights into many mechanical processes.

Force and Distance

Force and distance are fundamental to calculating work. In this exercise, the pallet is lifted using a force that counteracts gravity. The point to note here is that work is only done when the force has a component in the direction of movement—in this case, vertically upward.

• Force (F): The exercise gives a force of 575 Newtons, representing the weight of the pallet being lifted.
• Distance (d): The pallet is moved upward by 20 meters. Distance plays a critical role as it defines the extent over which the force is applied.

Multiplying these two, as shown in the exercise, gives us the total work done during this lifting process, calculated as 11,500 Joules.

Conversion of Units

In physics problems, unit conversion is often a necessary step to ensure that calculations are consistent and results are meaningful. The exercise ends with converting power from Watts to kilowatts, which is an example of changing measurement units to a more convenient scale or form.

• Time: Commonly measured in seconds but may need to be converted when considering longer durations.
• Power (P): Initially calculated in Watts, a standard unit of power.
• Conversion to Kilowatts: Since 1 kilowatt is 1,000 Watts, dividing 1150 Watts by 1,000 gives us 1.15 kilowatts, making the power more manageable for understanding larger scales.

This practice of conversion aids in comparing values across different systems and scales of magnitude, helping to solve and interpret both practical and theoretical problems.

Mechanical Work

Mechanical work is the energy transferred to or from an object via the application of force along a displacement. It's a cornerstone concept in understanding physical systems and energy changes.

• Mechanical work relates to changes in energy of a system due to applied forces.
• In the provided exercise, lifting the pallet is a clear example of work done against gravity.
• Expressed mathematically as Work = Force * Distance, it encapsulates the amount of energy transferred through force.

By computing work, we gain a quantitative grasp of how much energy is used or needed to move objects, thus bridging the gap between theoretical physics and real-world applications.