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Chapter 4: Problem 23

Show that the units of acceleration can be written as N/kg. Why does it make sense to give \(g\) as \(9.8 \mathrm{N} / \mathrm{kg}\) when talking about mass and weight?

Short Answer

Expert verified
The units of acceleration can indeed be written as N/kg. It makes sense to express 'g' as '9.8 N/kg' because the weight of an object (force due to gravity) is the product of its mass and the acceleration due to gravity. Hence, the unit of 'g' can also be expressed as 'N/kg'.

Step by step solution

01

Understanding Units

The units given, N and kg, represent Newtons and kilograms respectively. A Newton is the SI unit of force and a kilogram is the SI unit of mass.
02

Definition of Force

Remember that Force (in Newtons) is defined as the product of mass (in kilograms) and acceleration (in m/s^2), you can express this mathematically as F = ma
03

Unit of Acceleration Based on Definition

Given the formula from step 2, you can express acceleration as a = F/m. This implies that the units of acceleration can be expressed in N/kg.
04

Relation to Gravity

The gravitational force acting on an object is equal to the mass of the object multiplied by the gravitational acceleration (g). This force is the weight of the object. Hence, the gravitational acceleration (g) can be expressed as the weight of the object divided by its mass, which gives the unit N/kg.

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Most popular questions from this chapter

In a front-end collision, a \(1300-\mathrm{kg}\) car with shock-absorbing bumpers can withstand a maximum force of \(65 \mathrm{kN}\) before damage occurs. If the maximum speed for a nondamaging collision is \(10 \mathrm{km} / \mathrm{h},\) by how much must the bumper be able to move relative to the car?

A child pulls an 11 -kg wagon with a horizontal handle whose mass is \(1.8 \mathrm{kg},\) accelerating the wagon and handle at \(2.3 \mathrm{m} / \mathrm{s}^{2}\) Find the tension forces at each end of the handle. Why are they different?

Kinesin is a "motor protein" responsible for moving materials within living cells. If it exerts a 6.0 -pN force, what acceleration will it give a molecular complex with mass \(3.0 \times 10^{-18} \mathrm{kg} ?\)

A \(35-\mathrm{N}\) force is applied to a spring with spring constant \(k=220 \mathrm{N} / \mathrm{m} .\) How much does the spring stretch?

A small plane accelerates down the runway at \(7.2 \mathrm{m} / \mathrm{s}^{2} .\) If its propeller provides an \(11-\mathrm{kN}\) force, what's the plane's mass?
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