Answer:
![v=1.5m/s](https://tex.z-dn.net/?f=v%3D1.5m%2Fs)
Explanation:
The gravitational potential energy gets transformed into translational and rotational kinetic energy, so we can write
. Since
(the ball rolls without slipping) and for a solid sphere
, we have:
![mgh=\frac{mv^2}{2}+\frac{2mr^2\omega^2}{2*5}=\frac{mv^2}{2}+\frac{mv^2}{5}=\frac{7mv^2}{10}](https://tex.z-dn.net/?f=mgh%3D%5Cfrac%7Bmv%5E2%7D%7B2%7D%2B%5Cfrac%7B2mr%5E2%5Comega%5E2%7D%7B2%2A5%7D%3D%5Cfrac%7Bmv%5E2%7D%7B2%7D%2B%5Cfrac%7Bmv%5E2%7D%7B5%7D%3D%5Cfrac%7B7mv%5E2%7D%7B10%7D)
So our translational speed will be:
![v=\sqrt{\frac{10gh}{7}}=\sqrt{\frac{10(9.8m/s^2)(0.161m)}{7}}=1.5m/s](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7B10gh%7D%7B7%7D%7D%3D%5Csqrt%7B%5Cfrac%7B10%289.8m%2Fs%5E2%29%280.161m%29%7D%7B7%7D%7D%3D1.5m%2Fs)
The answer is C. F=ma basically says that force is a function of mass multiplied by acceleration. The first two answers don’t make sense because there’s no necessary relationship between mass and acceleration. And for the last two, the higher the mass, the higher the force needed, therefore C is the correct answer.
Answer:
![6.66\cdot 10^{-12}T](https://tex.z-dn.net/?f=6.66%5Ccdot%2010%5E%7B-12%7DT)
Explanation:
The magnetic field produced by a current-carrying wire is given by
![B=\frac{\mu_0 I}{2\pi r}](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B%5Cmu_0%20I%7D%7B2%5Cpi%20r%7D)
where
is the vacuum permeability
I is the current
r is the distance from the wire
In this problem we have
![I=0.040 \mu A=4\cdot 10^{-8}A](https://tex.z-dn.net/?f=I%3D0.040%20%5Cmu%20A%3D4%5Ccdot%2010%5E%7B-8%7DA)
r = 1.2 mm = 0.0012 m
So the magnetic field strength is
![B=\frac{(4\pi \cdot 10^{-7} H/m)(4\cdot 10^{-8}A)}{2\pi (0.0012 m)}=6.66\cdot 10^{-12}T](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B%284%5Cpi%20%5Ccdot%2010%5E%7B-7%7D%20H%2Fm%29%284%5Ccdot%2010%5E%7B-8%7DA%29%7D%7B2%5Cpi%20%280.0012%20m%29%7D%3D6.66%5Ccdot%2010%5E%7B-12%7DT)
It is the energy an object has because of its motion.