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Chapter 1: Problem 2

An object weighs \(25 \mathrm{kN}\) at a location where the acceleration of gravity is \(9.8 \mathrm{~m} / \mathrm{s}^{2}\). Determine its mass, in \(\mathrm{kg}\).

Short Answer

Expert verified
The mass of the object is approximately 2551 kg.

Step by step solution

01

Identify Given Values

The weight of the object is given as 25 kN. The acceleration due to gravity is given as 9.8 m/s虏.
02

Convert Kilonewtons to Newtons

Convert the weight from kilonewtons (kN) to newtons (N) because 1 kN = 1000 N. Therefore, the weight, W, is 25 kN * 1000 = 25000 N.
03

Use the Formula for Weight

Recall the formula for weight: \[ W = mg \] where W is the weight, m is the mass, and g is the acceleration due to gravity.
04

Rearrange the Formula

To find the mass, rearrange the formula to solve for m: \[ m = \frac{W}{g} \]
05

Plug in the Values

Insert the known values into the formula: \[ m = \frac{25000 \, \text{N}}{9.8 \, \text{m/s}^2} \]
06

Calculate the Mass

Perform the division to find the mass: \[ m \approx 2551 \, \text{kg} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Weight and Mass
First, let's differentiate between weight and mass, as they are related but distinct concepts. Weight is the force exerted on an object due to gravity and is measured in newtons (N). On the other hand, mass is the amount of matter in the object and is measured in kilograms (kg).
Weight is calculated by the formula: \ W = mg \ where \( W \) represents weight, \( m \) represents mass, and \( g \) represents the acceleration due to gravity.
Remember, your weight can change based on your location (for example, on the moon vs. Earth) because the gravitational pull varies. However, your mass remains constant.
Acceleration Due to Gravity
The acceleration due to gravity, denoted by \( g \), is the rate at which objects accelerate towards the center of a massive body, such as the Earth. Its standard value on Earth is approximately \( 9.8 \, \text{m/s}^2 \).
This value can vary slightly based on your position on the Earth's surface due to factors like altitude and Earth's rotation. It鈥檚 crucial to use the correct value of \( g \) for your specific location in calculations to obtain accurate results.
In our problem, we use \( 9.8 \, \text{m/s}^2 \) since it's the typical value used for Earth's gravitational acceleration.
Unit Conversion in Physics
Unit conversion is an important step in physics problems to ensure consistency in calculations. In this exercise, the weight was initially provided in kilonewtons (kN). Since standard calculations use newtons (N), we need to convert it.
\ 1 \, \text{kN} = 1000 \, \text{N} \
Thus, \( 25 \, \text{kN} \) converts to \( 25000 \, \text{N} \).
Always make sure your units are consistent when inserting values into formulas. This practice avoids errors and ensures the correctness of your answer.
Formula Manipulation
Formula manipulation is the process of rearranging mathematical equations to isolate the desired variable. For our exercise, we started with the weight formula: \ W = mg \
Since we needed to find the mass \( m \), we rearranged this formula. Dividing both sides by \( g \) gives: \ m = \frac{W}{g} \
Formula manipulation is crucial in physics to solve for unknown variables. It ensures we correctly isolate and identify what we need to find.

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Most popular questions from this chapter

A system consists of nitrogen \(\left(\mathrm{N}_{2}\right)\) in a piston- cylinder assembly, initially at \(p_{1}=140 \mathrm{kPa}\), and occupying a volume of \(0.068 \mathrm{~m}^{3}\). The nitrogen is compressed to \(p_{2}=690 \mathrm{kPa}\) and a final volume of \(0.041 \mathrm{~m}^{3} .\) During the process, the relation between pressure and volume is linear. Determine the pressure, in \(\mathrm{kPa}\), at an intermediate state where the volume is \(0.057 \mathrm{~m}^{3}\), and sketch the process on a graph of pressure versus volume.

Convert the following temperatures from \({ }^{\circ} \mathrm{C}\) to \(\mathrm{K}:\) (a) \(21^{\circ} \mathrm{C}\). (b) \(-40^{\circ} \mathrm{C}\), (c) \(500^{\circ} \mathrm{C}\), (d) \(0^{\circ} \mathrm{C}\), (e) \(100^{\circ} \mathrm{C}\), (f) \(-273.15^{\circ} \mathrm{C}\).

A \(2.2 \mathrm{~m}^{3}\) tank contains water vapor at \(10340 \mathrm{kPa}\) and \(633 \mathrm{~K}\). If the pressure, \(p\), specific volume, \(v\), and temperature, \(T\), of water vapor are related by the expression $$ p=[(7183.04) T /(v-0.0169)]-\left(25.02 \times 10^{3}\right) / v^{2} $$ where \(v\) is in \(\mathrm{m}^{3} / \mathrm{kg}, T\) is in \(\mathrm{K}\), and \(p\) is in \(\mathrm{kPa}\), determine the mass of water in the tank. Also, plot pressure versus specific volume for the isotherms \(T=667,778\), and \(889 \mathrm{~K}\).

Early commercial vapor power plants operated with turbine inlet conditions of about 12 bar and \(200^{\circ} \mathrm{C}\). Plants are under development today that can operate at over 34 MPa, with turbine inlet temperatures of \(650^{\circ} \mathrm{C}\) or higher. How have steam generator and turbine designs changed over the years to allow for such increases in pressure and temperature? Discuss.

Estimate the magnitude of the force, in \(\mathrm{N}\), exerted by a seat, belt on a \(100 \mathrm{~kg}\) driver during a frontal collision that decelerates. a car from \(1.5 \mathrm{~km} / \mathrm{h}\) to rest in \(0.1 \mathrm{~s}\). Express the car's deceleration in multiples of the standard acceleration of gravity, or \(g \mathrm{~s}\).
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