A charged particle of mass 8.39×10−4 kg starts from rest and accelerates through a potential difference of +25,000 V to reach a speed of 1170 m/s. What is the charge on this particle?
QV= 1/2(mv^2)
Q is the charge
V= potential
V= speed
m= mass
Q * 25000= 0.5 * 0.000839* 1170* 1170
Q= 574/ 25000= 0.023 C
See if this can help
To find the charge on the particle, we can use the formula for the final kinetic energy of a charged particle accelerated through a potential difference:
K.E. = (1/2)mv^2
where K.E. is the kinetic energy, m is the mass of the particle, and v is the final velocity of the particle.
We know the final velocity of the particle (v = 1170 m/s) and the mass of the particle (m = 8.39×10^−4 kg), so we can substitute these values into the equation:
K.E. = (1/2)(8.39×10^−4 kg)(1170 m/s)^2
Next, we can calculate the kinetic energy:
K.E. = (1/2)(8.39×10^−4 kg)(1368900 m^2/s^2)
K.E. ≈ 576.77 J
Now, we can use the relationship between potential difference and kinetic energy for a charged particle:
K.E. = qV
where K.E. is the kinetic energy, q is the charge on the particle, and V is the potential difference.
We know the potential difference (V = +25,000 V) and the kinetic energy (K.E. ≈ 576.77 J), so we can rearrange the equation and solve for the charge (q):
q = K.E. / V
q = 576.77 J / 25,000 V
q ≈ 0.0231 C
Therefore, the charge on the particle is approximately 0.0231 Coulombs.