Question

Use Einstein’s energy equation to solve the following problem. Recall that the speed of light is 3 × 108 m/s.

If a 5.0-kg stone is completely converted to energy, what is its energy equivalent in joules?

4.5 × 10^17 J
1.5 × 10^10 J
1.5 × 10^9 J
4.5 × 10^15 J

Answer 1

@jim_thompson5910

Answer 2

@anyone

Answer 3

\(\sf E= mc^2\) , where m is the mass (5 kg) & c is the speed of light ( 3 × 108 m/s) .

All you have to do is substitute the given values.

Answer 4

i am not to good with that equation

Answer 5

Given info
\[\Large m = 5\]
\[\Large c = 3 \times 10^8\]
plug them into the formula
\[\Large E = mc^2\]
\[\Large E = 5*\left(3 \times 10^8\right)^2\]
then evaluate

Answer 6

oh ok

Answer 7

(15*50^8)^2

Answer 8

btw,

\[\Large 3 \times 10^8 = 300,000,000\]

which is the number `300 million`

Answer 9

PEMDAS says you have to do exponents before multiplication

Answer 10

you cannot multiply the 5 and 3 because the 3 is under an exponent

Answer 11

ok then can u show me? i am confused

Answer 12

Like i said not too good with this formula

Answer 13

\[\Large E = 5*\left(3 \times 10^8\right)^2\]
\[\Large E = 5*\left(3\right)^2*\left(10^8\right)^2\]
\[\Large E = 45*\left(10^8\right)^2\]
I'll let you finish up

Answer 14

45*10^10 ?

Answer 15

you won't add the exponents in this case

Answer 16

how?

Answer 17

when you raise an exponential expression to another exponent, you multiply the exponents

Answer 18

example:
\[\Large (2^3)^5 = 2^{3*5} = 2^{15}\]

Answer 19

ok so 8*2= 45*10^16

Answer 20

now convert \[\Large 45 \times 10^{16}\] to scientific notation

Answer 21

4.5*10^16 ???

Answer 22

no

Answer 23

then what??

Answer 24

it might help to think of 45 as 4.5*10^1

Answer 25

ok?

Answer 26

\[\Large 45*10^{16} = (4.5 \times 10^1)*10^{16} = ??\]

Answer 27

the 10^16 is multiplied by 4.5 and 10^1 yes??

Answer 28

what is 10^1 times 10^16 equal to?

in terms of an exponential expression

Answer 29

4.5*10^17

Answer 30

correct

Answer 31

ok thanks