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4.7* Near to the point where I am standing on the surface of Planet X, the gravitational force on a mass m is vertically down but has magnitude myy2 where y is a constant and y is the mass's height above the horizontal ground. (a) Find the work done by gravity on a mass m moving from r₁ to r2, and use your answer to show that gravity on Planet X, although most unusual, is still conservative. Find the corresponding potential energy. (b) Still on the same planet, I thread a bead on a curved, frictionless, rigid wire, which extends from ground level to a height h above the ground. Show clearly in a picture the forces on the bead when it is somewhere on the wire. (Just name the forces so it's clear what they are; don't worry about their magnitude.) Which of the forces are conservative and which are not? (c) If I release the bead from rest at a height h, how fast will it be going when it reaches the ground?

4.7* Near to the point where I am standing on the surface of Planet X, the gravitational force on a mass m is vertically down but has magnitude myy2 where y is a constant and y is the mass's height above the horizontal ground. (a) Find the work done by gravity on a mass m moving from r₁ to r2, and use your answer to show that gravity on Planet X, although most unusual, is still conservative. Find the corresponding potential energy. (b) Still on the same planet, I thread a bead on a curved, frictionless, rigid wire, which extends from ground level to a height h above the ground. Show clearly in a picture the forces on the bead when it is somewhere on the wire. (Just name the forces so it's clear what they are; don't worry about their magnitude.) Which of the forces are conservative and which are not? (c) If I release the bead from rest at a height h, how fast will it be going when it reaches the ground?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem 4.7** Near to the point where I am standing on the surface of Planet X, the gravitational force on a mass \( m \) is vertically down but has magnitude \( m \gamma y^2 \) where \( \gamma \) is a constant and \( y \) is the mass’s height above the horizontal ground. **(a)** Find the work done by gravity on a mass \( m \) moving from \( r_1 \) to \( r_2 \), and use your answer to show that gravity on Planet X, although most unusual, is still conservative. Find the corresponding potential energy. **(b)** Still on the same planet, I thread a bead on a curved, frictionless, rigid wire, which extends from ground level to a height \( h \) above the ground. Show clearly in a picture the forces on the bead when it is somewhere on the wire. (Just name the forces so it’s clear what they are; don’t worry about their magnitude.) Which of the forces are conservative and which are not? **(c)** If I release the bead from rest at a height \( h \), how fast will it be going when it reaches the ground?
Transcribed Image Text:**Problem 4.7** Near to the point where I am standing on the surface of Planet X, the gravitational force on a mass \( m \) is vertically down but has magnitude \( m \gamma y^2 \) where \( \gamma \) is a constant and \( y \) is the mass’s height above the horizontal ground. **(a)** Find the work done by gravity on a mass \( m \) moving from \( r_1 \) to \( r_2 \), and use your answer to show that gravity on Planet X, although most unusual, is still conservative. Find the corresponding potential energy. **(b)** Still on the same planet, I thread a bead on a curved, frictionless, rigid wire, which extends from ground level to a height \( h \) above the ground. Show clearly in a picture the forces on the bead when it is somewhere on the wire. (Just name the forces so it’s clear what they are; don’t worry about their magnitude.) Which of the forces are conservative and which are not? **(c)** If I release the bead from rest at a height \( h \), how fast will it be going when it reaches the ground?
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