/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 Calculate the downward pressure ... [FREE SOLUTION] | 91Ó°ÊÓ

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Calculate the downward pressure due to gravity exerted by the bottom face of a \(1.00 \mathrm{kg}\) cube of iron that is \(5.00 \mathrm{cm}\) on a side.

Short Answer

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Answer: The downward pressure exerted by the bottom face of the cube is 3924 N/m².

Step by step solution

01

Find the weight of the cube

The weight of the cube is the force exerted by gravity on its mass. We can find this using the formula for gravitational force: F = m * g, where F is the force (weight), m is the mass, and g is the acceleration due to gravity. We are given the mass (1.00 kg), and the acceleration due to gravity is about 9.81 m/s². Weight (F) = m * g = 1.00 kg * 9.81 m/s² = 9.81 N
02

Find the area of the bottom face of the cube

The area of the bottom face is equal to side length (L) squared. We are given the side length (5.00 cm) but we need to convert it to meters (m). L = 5.00 cm = 0.0500 m Area (A) = L^2 = (0.0500 m)^2 = 0.002500 m²
03

Calculate the pressure exerted by the cube

Pressure is defined as the force exerted on a surface divided by the area of the surface. In this case, the pressure is exerted by the weight of the cube on the bottom face. Pressure (P) = Weight (F) / Area (A) = 9.81 N / 0.002500 m² = 3924 N/m² The downward pressure due to gravity exerted by the bottom face of the cube is 3924 N/m².

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Key Concepts

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

Understanding Gravitational Force
Gravitational force is a fundamental concept in physics, describing the pull that objects exert on one another due to their mass. Everything with mass feels this force, and it is what keeps us rooted on Earth. Sir Isaac Newton quantified this attraction with his law of universal gravitation, which states that every point mass attracts each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

When dealing with objects near Earth's surface, we simplify the concept by using the constant acceleration due to gravity, denoted as \( g \). This is approximately \( 9.81 \text{m/s}^2 \), and it allows us to calculate the weight of an object – which is just the gravitational force acting on a body due to Earth's mass. The formula to find the weight (gravitational force) of an object is \( F = m \times g \), where \( m \) is the mass of the object and \( g \) the acceleration due to gravity.

In our exercise, the 1.00 kg cube of iron is attracted to Earth with a gravitational force which equals its weight, computed simply as:
Applying Newton's Second Law
Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. The law is often expressed as the equation \( F = ma \), where \( F \) is the force applied, \( m \) the mass of the object, and \( a \) the acceleration. This principle not only applies to cases of objects being pushed or pulled but also fundamentally describes how gravitational force acts as a weight.

In practical terms, we often use this second law to calculate the force (or weight) of an object by multiplying its mass by the acceleration due to gravity, thus combining Newton's law with the force of gravity. In the context of the exercise provided, the iron cube's weight is a direct application of Newton's second law: the gravitational force acting on the cube is the product of its mass and gravitational acceleration.
Calculating Pressure
Pressure calculation is crucial in various scientific and engineering fields. It represents the perpendicular force per unit area applied on a surface and is measured in pascals (Pa) in the metric system. The formula for pressure is:\[ P = \frac{F}{A} \], where \( P \) is the pressure, \( F \) the force, and \( A \) the area over which the force is distributed.

For example, when looking at the cube from our exercise, we calculate the area of the bottom face, which is the side length squared. With the weight and area known, we then divide the weight by the area. This gives us the pressure exerted by the cube on the surface it rests upon. The pressure is significant for understanding how structures support loads, how fluids behave under different conditions, and even in medical applications where blood pressure is a critical health metric. Ensuring that students grasp this concept is fundamental for their progression in physics and related disciplines.

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Most popular questions from this chapter

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