What is the speed of a proton whose kinetic energy is 36.0 MeV?
I don’t know if I did my calculations right but V^2 I got 6.89 *10^15, how do I get V on its own? I square rooted and got 2.62 *10^15 but that’s not correct. Answer is supposed to be 8.31 * 10^7 m/S.
(1/2)m v^2 = Kinetic energy
if 6.89 *10^15 were correct for v^2
then you need an even n in 10^n to take the square root
for example
68.9 * 10^14
that would give you 8.3 * 10^7
sqrt z^n = z^(n/2)
like sqrt 10,000 = 100
is
sqrt 10^4 = 10^2
.... but you knew that, right ? :)
To find the speed of a proton whose kinetic energy is 36.0 MeV, you can use the following steps:
1. First, convert the kinetic energy from MeV to joules. 1 MeV is equal to 1.6 x 10^-13 joules. So, 36.0 MeV is equal to 36.0 x 1.6 x 10^-13 joules.
36.0 MeV = 36.0 x 1.6 x 10^-13 J = 5.76 x 10^-12 J
2. The kinetic energy (K) of a particle can be calculated using the formula:
K = (1/2)mv^2
where m is the mass of the particle and v is its velocity.
3. The mass of a proton is approximately 1.67 x 10^-27 kg.
4. Rearrange the formula to solve for velocity (v):
v = √((2K) / m)
5. Plug in the values into the formula:
v = √((2 * 5.76 x 10^-12 J) / (1.67 x 10^-27 kg))
Calculating this expression, you should get:
v ≈ 8.31 x 10^7 m/s
So, the correct speed of a proton with a kinetic energy of 36.0 MeV is 8.31 x 10^7 m/s.
To calculate the speed of a proton based on its kinetic energy, we can use the following equation:
Kinetic energy = (1/2) * mass * velocity^2
In this case, we are given the kinetic energy of the proton as 36.0 MeV. We need to convert this energy to joules before proceeding with the calculation.
1 MeV is equal to 1.6 x 10^-13 joules.
So, 36.0 MeV = 36.0 x 1.6 x 10^-13 joules = 5.76 x 10^-12 joules.
Now, rearranging the equation, we get:
velocity^2 = (2 * kinetic energy) / mass
To find the velocity, we need to take the square root of both sides of the equation.
velocity = sqrt((2 * kinetic energy) / mass)
The mass of a proton is approximately 1.67 x 10^-27 kg.
Now plug in the values into the equation:
velocity = sqrt((2 * 5.76 x 10^-12 joules) / (1.67 x 10^-27 kg))
Calculating this, we get velocity = 8.31 x 10^7 m/s (rounded to 3 significant figures).
So, the correct answer for the speed of the proton is indeed 8.31 x 10^7 m/s.