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3 years ago

10

A pinball bangs against a bumper giving the ball a speed of 42cm/s if the ball has a mass of 50.0g what is the ball’s kinetic en

ergy in joules

1 answer:

Ann [662]3 years ago

7 0

Explanation:

<h3><u>Given</u><u>:</u><u>-</u></h3>

mass=50g

velocity=42cm/s

<h3><u>To</u><u> </u><u>find</u><u>:</u><u>-</u></h3>

Kinetic energy

<h3><u>Solution</u><u>:</u><u>-</u></h3>

As we know that

${\boxed{\sf kinetic\:energy={\dfrac {1}{2}}mv^2}}$

Substitute the values

${:}\longrightarrow$ $\sf k.v={\dfrac {1}{{\cancel{2}}}}\times 50\times {\cancel{42}}^2$

${:}\longrightarrow$ $\sf k.v=50\times 21^2$

${:}\longrightarrow$ $\sf k.v=50×441$

${:}\longrightarrow$ $\sf k.v=22050MJ$

1Joule=1000milijoules
22050MJ= ${\dfrac {22050}{1000}}=22.05J$
=22J(Approximately)

$\therefore$ ${\underline{\boxed{\bf Kinetic\:energy=22Joule}}}$

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Answer with Explanation:

Mass of block=1.1 kg

Th force applied on block is given by

F(x)= $(2.4-x^2)\hat{i}N$

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Initial kinetic energy= $K_i=\frac{1}{2}mv^2_i=\frac{1}{2}(1.1)(0)=0$

Work energy theorem:

$K_f-K_i=W$

Where $K_f=$ Final kinetic energy

$K_i$ =Initial kinetic energy

$W=Total work done$

Substitute the values then we get

$K_f-0=\int_{0}^{2}F(x)dx$

Because work done= $Force\times displacement$

$K_f=\int_{0}^{2}(2.4-x^2)dx$

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When the kinetic energy is maximum then $\frac{dK}{dx}=0$

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$\frac{d^2K}{dx^2}=-2x$

Substitute x= $\sqrt{2.4}$

$\frac{d^2K}{dx^2}=-2\sqrt{2.4}$

Substitute x= $-\sqrt{2.4}$

$\frac{d^2K}{dx^2}=2\sqrt{2.4}>0$

Hence, the kinetic energy is maximum at x= $\sqrt{2.4}$

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