Answer:
Magnetic field, ![B=2.55\times 10^{-14}\ T](https://tex.z-dn.net/?f=B%3D2.55%5Ctimes%2010%5E%7B-14%7D%5C%20T)
Explanation:
It is given that,
Speed of proton, ![v=4\times 10^6\ m/s](https://tex.z-dn.net/?f=v%3D4%5Ctimes%2010%5E6%5C%20m%2Fs)
Mass of the proton, ![m=1.67\times 10^{-27}\ kg](https://tex.z-dn.net/?f=m%3D1.67%5Ctimes%2010%5E%7B-27%7D%5C%20kg)
Charge on proton, ![q=1.6\times 10^{-19}\ C](https://tex.z-dn.net/?f=q%3D1.6%5Ctimes%2010%5E%7B-19%7D%5C%20C)
We need to find the magnetic field strength required to just balance the weight of the proton and keep it moving horizontally.
The Lorentz force is given by :
.............(1)
The weight of proton,
..............(2)
From equation (1) and (2), we get :
![mg=qvB](https://tex.z-dn.net/?f=mg%3DqvB)
![B=\dfrac{mg}{qv}](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7Bmg%7D%7Bqv%7D)
![B=\dfrac{1.67\times 10^{-27}\ kg\times 9.8\ m/s^2}{1.6\times 10^{-19}\ C\times 4\times 10^6\ m/s}](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B1.67%5Ctimes%2010%5E%7B-27%7D%5C%20kg%5Ctimes%209.8%5C%20m%2Fs%5E2%7D%7B1.6%5Ctimes%2010%5E%7B-19%7D%5C%20C%5Ctimes%204%5Ctimes%2010%5E6%5C%20m%2Fs%7D)
![B=2.55\times 10^{-14}\ T](https://tex.z-dn.net/?f=B%3D2.55%5Ctimes%2010%5E%7B-14%7D%5C%20T)
Hence, this is the required solution.
Answer:
4.4 m/s
Explanation:
momentum is always conserved so we can use conversation of momentum to solve the question, also momentum is a vector quantity ( it has magnitude and direction) which is the product of the bodies mass and velocity.
conservation law of momentum relates by the formula below:
momentum before collision = momentum after collision
M1U1 + M2U2 = M1V1 + M2V2
in the case of this two, the formula becomes
M1U1 + M2U2 = V (M1 + M2) since she jumped into his arm
there masses are M1 = 75.6 kg M2 = 59 kg and their velocities are U1 = 3.7 m/s and U2 = 5.4 m/s, their common velocity after collision = V since their motion is backward the formula becomes
-M1U1 - M2U2 = V(M1 + M2)
substitute the values into the equations
(-75.6 × 3.7 ) + (- 59 × 5.4) = V ( 75.6 + 59)
- 598.32 = 134.6 V
divide both side by 134.6
V = - 598.32 / 134.6 = -4.445 m/s = -4.4 m/s to nearest tenth the negative means in the same backward direction
I haven't worked out the number, but it won't be necessary ... it's easy to pick the answer out of the choices that are given. ... The time (5 yrs) is less than the half-life (12.35 yrs), so more than half of the original sample (100mg) remains. Only one of the choices is more than 50 mg. (Can you find it ?)
C : perpendicular
The component of a vector are perpendicular