Answer:
T = 11.93 N
Explanation:
Newton's second law to the puck in the circular path
∑F = m*a Formula (1)
∑F : algebraic sum of the forces in radial direccion (N)
m : puck mass (kg)
a : radial acceleration of the puck (m/s²)
Data:
m = 0.085 kg
L = 0.72 m = R : radium of the circular path (m)
θ= one revolution = 2Π rad
t= 0.45 s
Angular speed of the puck
ω = θ/t
ω = 1 rev/0.45 s = (2π/0.45) rad/s
ω = 13.96 rad /s
Radial acceleration or centripetal
a = ω²*R
a = (13.96) ²* (0.72)
a = 140.3 m/s²
Magnitude of the tension in the string (T)
We apply the Formula (1)
∑F = m*a
T = (0.085 kg )* (140.3 m/s² )
T = 11.93 N
Answer:
The angle between the blue beam and the red beam in the acrylic block is

Explanation:
From the question we are told that
The refractive index of the transparent acrylic plastic for blue light is 
The wavelength of the blue light is 
The refractive index of the transparent acrylic plastic for red light is 
The wavelength of the red light is 
The incidence angle is 
Generally from Snell's law the angle of refraction of the blue light in the acrylic block is mathematically represented as
![r_F = sin ^{-1}[\frac{sin(i) * n_a }{n_F} ]](https://tex.z-dn.net/?f=r_F%20%3D%20%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bsin%28i%29%20%2A%20%20n_a%20%7D%7Bn_F%7D%20%5D)
Where
is the refractive index of air which have a value of
So
![r_F = sin ^{-1}[\frac{sin(45) * 1 }{ 1.497} ]](https://tex.z-dn.net/?f=r_F%20%3D%20%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bsin%2845%29%20%2A%20%201%20%7D%7B%201.497%7D%20%5D)

Generally from Snell's law the angle of refraction of the red light in the acrylic block is mathematically represented as
![r_C = sin ^{-1}[\frac{sin(i) * n_a }{n_C} ]](https://tex.z-dn.net/?f=r_C%20%3D%20%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bsin%28i%29%20%2A%20%20n_a%20%7D%7Bn_C%7D%20%5D)
Where
is the refractive index of air which have a value of
So
![r_C = sin ^{-1}[\frac{sin(45) * 1 }{ 1.488} ]](https://tex.z-dn.net/?f=r_C%20%3D%20%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bsin%2845%29%20%2A%20%201%20%7D%7B%201.488%7D%20%5D)

The angle between the blue beam and the red beam in the acrylic block

substituting values


This is very good conceptual question and can clear your doubts regarding work-energy theorem.
Whenever force is perpendicular to the direction of the motion, work done by that force is zero.
According to work-energy theorem,
Work done by all the force = change in kinetic energy.
here, work done = 0.
Therefore,
0=change in kinetic energy
This means kinetic energy remains constant.
Hope this helps
Since speed (v) is in ft/sec, let's convert our diameters from inches to feet:
1) 5/8in = 0.625in
0.625in × 1ft/12in = 0.0521ft
2) 0.25in × 1ft/12in = 0.021ft
Equation:






new velocity coming out of the hose then is
44 ft/sec
The answer is 96 N .....................................