Question

A stone of mass 150g is thrown upwards with a velocity 35m/s. What is the maximum potential energy that can be gained by the stone?​

Answer 1

Answer:

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Answer 2

Answer:

Given :-

• A stone of mass 150 g is thrown upwards with a velocity of 35 m/s.

To Find :-

• What is the maximum potential energy that can be gained by the stone.

Formula Used :-

$\clubsuit$ Third Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v^2 =\: u^2 + 2gh}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• g = Acceleration due to gravity
• h = Height

$\clubsuit$ Potential Energy Formula :

$\mapsto \sf\boxed{\bold{\pink{P.E =\: mgh}}}$

where,

• P.E = Potential Energy
• m = Mass
• g = Acceleration due to gravity
• h = Height

Solution :-

First, we have to find the height :

Given :

• Final Velocity (v) = 0 m/s
• Initial Velocity (u) = 35 m/s
• Acceleration due to gravity (g) = - 10 m/s²

According to the question by using the formula we get,

$\implies \sf (0)^2 =\: (35)^2 + 2(- 10)h$

$\implies \sf 0 \times 0 =\: 35 \times 35 + (- 20)h$

$\implies \sf 0 =\: 1225 - 20h$

$\implies \sf 0 - 1225 =\: - 20h$

$\implies \sf {\cancel{-}} 1225 =\: {\cancel{-}} 20h$

$\implies \sf 1225 =\: 20h$

$\implies \sf \dfrac{1225}{20} =\: h$

$\implies \sf 61.25 =\: h$

$\implies \sf\bold{\purple{h =\: 61.25\: m}}$

Now, we have to convert the mass g into kg :

$\implies \sf Mass =\: 150\: g$

$\implies \sf Mass =\: \dfrac{150}{1000}\: kg\: \: \bigg\lgroup \sf\bold{\pink{1\: g =\: \dfrac{1}{1000}\: kg}}\bigg\rgroup$

$\implies \sf\bold{\purple{Mass =\: 0.15\: kg}}$

Now, we have to find the maximum potential energy that can be gained by the stone :

Given :

• Mass (m) = 0.15 kg
• Acceleration due to gravity (g) = 10 m/s²
• Height (h) = 61.25 m

According to the question by using the formula we get,

$\longrightarrow \sf P.E =\: (0.15)(10)(61.25)$

$\longrightarrow \sf P.E =\: 0.15 \times 10 \times 61.25$

$\longrightarrow \sf P.E =\: 1.5 \times 61.25$

$\longrightarrow \sf\bold{\red{P.E =\: 91.875\: J}}$

${\small{\bold{\underline{\therefore\: The\: maximum\: potential\: energy\: that\: can\: be\: gained\: by\: the\: stone\: is\: 91.875\: J\: .}}}}$