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Q.49

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 711

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Short Answer

A group of science and engineering students embarks on a quest to make an electrostatic projectile launcher. For their first trial, a horizontal, frictionless surface is positioned next to the 12-cm-diameter sphere of a Van de Graaff generator, and a small, 5.0 g plastic cube is placed on the surface with its center 2.0 cm from the edge of the sphere. The cube is given a positive charge, and then the Van de Graaff generator is turned on, charging the sphere to a potential of 200,000 V in a negligible amount of time. How much charge does the plastic cube need to achieve a final speed of a mere 3.0 m/s? Does this seem like a practical projectile launcher?

The required Charge is 150 nC

See the step by step solution

Step by Step Solution

Step 1: Energy Conversion Law

As per the law of energy conversations, within a closed system energy remains same. Energy cannot be destroyed or created it only transform from one form to another.

The expression in this electric potential is;

Here in in equation K is column's constant and q is the charge where r denote as distance.

Hence;

Step 2: Given Data

Here;

Sphere potential is 200,000 V

d =12 cm, hence r= 6 cm

and k= 9 x 109 Nm2/C2

Step 3: Required Charge Calculation 

As per the given Condition distance is;

d=2 cm+ 6cm =8 cm

hence the potential difference is;

Substituting all the given data along with the distance of condition;

As law of energy conversations;

kinetic energy is equal to potential energy

As per given condition m= 5g; v= 3 m/s

Hence;

Hence the required charge can be considered as 150 nC

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