The rest mass of a particle is 10^-24kg.It is moving with a velocity of 1.8*10^18m/s. Calculate its mass when it is in motion.
To calculate the mass of a particle when it is in motion, we will use the relativistic formula for mass:
m = m0 / sqrt(1 - v^2/c^2)
Where:
m0 is the rest mass of the particle (given as 10^-24 kg),
v is the velocity of the particle (given as 1.8 * 10^18 m/s), and
c is the speed of light (approximately 3 * 10^8 m/s).
Let's plug in the values and calculate:
m = (10^-24 kg) / sqrt(1 - (1.8 * 10^18 m/s)^2 / (3 * 10^8 m/s)^2)
Now we simplify the expression:
m = (10^-24 kg) / sqrt(1 - (1.8 * 10^18)^2 / (3 * 10^8)^2)
m = (10^-24 kg) / sqrt(1 - (3.24 * 10^36) / (9 * 10^16))
m = (10^-24 kg) / sqrt(1 - 3.6 * 10^19)
m = (10^-24 kg) / sqrt(1 - 3.6 * 10^19)
m = (10^-24 kg) / sqrt(-3.6 * 10^19 + 1)
m = (10^-24 kg) / sqrt(-3.6 * 10^19 + 1)
Notice that in the denominator, we have a square root of a negative number. This is not physically meaningful, indicating that the particle cannot reach a velocity equal to or greater than the speed of light.
Therefore, we cannot calculate the mass of the particle when it is in motion.