Question

A ball of mass 100g is thrown vertically upwards with an initial velocity of 10m/s.Calculate
the maximum potential energy it gains as it goes up.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Mass of ball = 100g

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• Initial velocity = 10m/s

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$\red{\underline \bold{To \: Find:}}$

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• Maximum potential energy it gains

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Mass = 100g = 0.1kg

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• Velocity = 10m/s

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$\underline{\bold{\texttt{Mechanical energy when the ball was thrown :}}}$

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$\bf \dag \ \ Kinetic \ Energy + Potential \ Energy$

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As ball was thrown from the bottom so height will be "0" or negligible , hence potential energy at that point will be "0"

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$\bf \longmapsto \dfrac { 1 } { 2 } \times mv ^2 + 0$

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$\sf \longmapsto \dfrac { 1 } { 2 } \times 0.1 \times 10^2$

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$\sf \longmapsto \dfrac { 1 } { 2 } \times 1 \times 10$

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$\bf \dashrightarrow 5 \ J$ ------- (1)

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Hence Mechanical energy at the top will also be 5 J [ As energy is conserved ]

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$\underline{\bold{\texttt{Mechanical energy when the ball reaches maximum height :}}}$

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$\bf \dag \ \ Kinetic \ Energy + Potential \ Energy$

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As ball reaches its maximum height then the velocity of ball becomes "0" m/s because at that very moment the ball will be changing its direction i.e downwards from upwards so the kinetic energy at that point will be "0"

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$\sf \longmapsto 0 + Potential \ energy$

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$\bf \dashrightarrow Potential \ Energy$ ------ (2)

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$\underline{\bold{\texttt{From law of conservation of energy, </p><p>}}}$

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initial mechanical = Final mechanical energy $\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ energy

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(1) = (2)

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$\bf \dashrightarrow 5 = Potential \ Energy$

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• Hence maximum potential energy the ball can gain is at the highest point it can reach.

• So maximum potential energy in this case is 5 J

Answer 2

Given: The mass and initial velocity of the ball.

To find: Maximum potential energy of the ball going higher.

Step-by-step explanation:

• The rate of change of an object's position with respect to a frame of reference is its velocity, which is a function of time. A statement of an object's speed and direction of motion is referred to as velocity.

Solution:

⇒ $KE=\frac{1}{2}\times m\times v^{2}$ (KE is Kinetic Energy)

⇒ $KE=0.5\times 100\times 10\times10=5000$ joules

Total energy$=PE+KE$ (PE is Potential Energy)

∴ $PE+KE=5000J$

Due to the conservation of energy, total energy at point X must also be $5000J$. K.E must be zero for P.E to be maximal.

Hence, PE$=5000J$