Answer and explanation:
A.
Muon travelled straight down towards the earth. Therefore the tree moves up in the rest frame of muon (option a)
B.
In muon rest frame it travels Zero meters
C.
Distance, d = Velocity, v * Time, s
![where, v = 0.9c = 0.9 \times 8 \times 10^8 , s = 2.2 \mu s](https://tex.z-dn.net/?f=where%2C%20v%20%3D%200.9c%20%3D%200.9%20%5Ctimes%208%20%5Ctimes%2010%5E8%20%2C%20s%20%3D%202.2%20%5Cmu%20s)
![d = 0.9 \times 3 \times 10^8 \times 2.2 \times 10^{-6}\\\\d = 594m](https://tex.z-dn.net/?f=d%20%3D%200.9%20%5Ctimes%203%20%5Ctimes%2010%5E8%20%5Ctimes%202.2%20%5Ctimes%2010%5E%7B-6%7D%5C%5C%5C%5Cd%20%3D%20594m)
D.
Distance from the top of the mountain to the tree is the same as the distance travelled by the tree in the muons rest frame
that is same as in part C which is 594m
E.
Using lorentz contraction
In the rest frame of someone standing on the mountain
the distance is given by
![d' = \frac{d}{\gamma} = d\sqrt{1 - \frac{v^2}{c^2}}, where, \frac{1}{\gamma}= \sqrt{1 - \frac{v^2}{c^2}}](https://tex.z-dn.net/?f=d%27%20%3D%20%5Cfrac%7Bd%7D%7B%5Cgamma%7D%20%3D%20d%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%2C%20where%2C%20%5Cfrac%7B1%7D%7B%5Cgamma%7D%3D%20%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D)
![d' = 594\sqrt{1 - \frac{(0.9c)^2}{c^2}}](https://tex.z-dn.net/?f=d%27%20%3D%20594%5Csqrt%7B1%20-%20%5Cfrac%7B%280.9c%29%5E2%7D%7Bc%5E2%7D%7D)
![d' = 594\sqrt{1 - 0.81}](https://tex.z-dn.net/?f=d%27%20%3D%20594%5Csqrt%7B1%20-%200.81%7D)
![d' = 594 \times 0.4359](https://tex.z-dn.net/?f=d%27%20%3D%20594%20%5Ctimes%200.4359)
d' = 258.92m
F.
in the rest frame of someone standing on the mountain,
muon moves straight down
Answer:
(A) ![F_N - mg\cos\theta](https://tex.z-dn.net/?f=F_N%20-%20mg%5Ccos%5Ctheta)
Explanation:
The net force perpendicular to the surface of the incline is the sum of the gravity force component, which is mgcos(theta), and the reactionary normal force caused by the surface of the incline. The sum is F_N - mgcos(theta) and is usually 0 which is why the object is not moving perpendicularly to the surface of the incline.
Answer:
21.67 rad/s²
208.36538 N
Explanation:
= Final angular velocity = ![\dfrac{1}{6}78=13\ rad/s](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B6%7D78%3D13%5C%20rad%2Fs)
= Initial angular velocity = 78 rad/s
= Angular acceleration
= Angle of rotation
t = Time taken
r = Radius = 0.13
I = Moment of inertia = 1.25 kgm²
From equation of rotational motion
![\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\dfrac{13-78}{3}\\\Rightarrow \alpha=-21.67\ rad/s^2](https://tex.z-dn.net/?f=%5Comega_f%3D%5Comega_i%2B%5Calpha%20t%5C%5C%5CRightarrow%20%5Calpha%3D%5Cdfrac%7B%5Comega_f-%5Comega_i%7D%7Bt%7D%5C%5C%5CRightarrow%20%5Calpha%3D%5Cdfrac%7B13-78%7D%7B3%7D%5C%5C%5CRightarrow%20%5Calpha%3D-21.67%5C%20rad%2Fs%5E2)
The magnitude of the angular deceleration of the cylinder is 21.67 rad/s²
Torque is given by
![\tau=I\alpha\\\Rightarrow \tau=1.25\times -21.67\\\Rightarrow \tau=-27.0875](https://tex.z-dn.net/?f=%5Ctau%3DI%5Calpha%5C%5C%5CRightarrow%20%5Ctau%3D1.25%5Ctimes%20-21.67%5C%5C%5CRightarrow%20%5Ctau%3D-27.0875)
Frictional force is given by
![F=\dfrac{\tau}{r}\\\Rightarrow F=\dfrac{-27.0875}{0.13}\\\Rightarrow F=-208.36538\ N](https://tex.z-dn.net/?f=F%3D%5Cdfrac%7B%5Ctau%7D%7Br%7D%5C%5C%5CRightarrow%20F%3D%5Cdfrac%7B-27.0875%7D%7B0.13%7D%5C%5C%5CRightarrow%20F%3D-208.36538%5C%20N)
The magnitude of the force of friction applied by the brake shoe is 208.36538 N
Answer:
O- to track how fast a heart beats
Explanation:
1). D. Combined Gas Law
3.) D. Pressure and temperature
4.) C. Boyles law