Question

A particle having a speed of 0.87c has a momentum of 10-16 kg·m/s. what is its mass?

Answer 1

To find the mass of a particle with a given momentum and speed, we can use the relativistic momentum equation. We substitute the values into the equation and solve for the mass. Given a momentum of 10^-16 kg·m/s and a speed of 0.87c, we can calculate the mass of the particle.

Step-by-step explanation:

To find the mass of a particle, we can use the relativistic momentum equation:

p = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}}

Given that the momentum (p) is 10-16 kg·m/s and the speed (v) is 0.87c, we can substitute these values into the equation and solve for the mass (m).

First, we need to convert the speed to m/s.

0.87c = (0.87)(3.00 × 108 m/s) = 2.61 × 108 m/s

Now we can plug the values into the equation:

10^{-16} = m \cdot 2.61 × 10^{8} \cdot \sqrt{1 - \frac{(2.61 × 10^{8})^2}{(3.00 × 10^{8})^2}}

Solving this equation will give us the mass of the particle.

Answer 2

The momentum p of a moving particle is the product between its mass, m, and tis velocity, v:

`p=mv`
In our problem, we know
`p=10^(-16)~Kg \cdot m/s` and
`v=0.87c=0.87\cdot 3\cdot10^8~m/s=2.61\cdot 10^8~m/s`, and using the relationship mentioned above, we can find the mass m of the particle:

`m= (p)/(v) =3.8\cdot10^(-25)~Kg`