Answer:
vi = 4.77 ft/s
Explanation:
Given:
- The radius of the surface R = 1.45 ft
- The Angle at which the the sphere leaves
- Initial velocity vi
- Final velocity vf
Find:
Determine the sphere's initial speed.
Solution:
- Newton's second law of motion in centripetal direction is given as:
m*g*cos(θ) - N = m*v^2 / R
Where, m: mass of sphere
g: Gravitational Acceleration
θ: Angle with the vertical
N: Normal contact force.
- The sphere leaves surface at θ = 34°. The Normal contact is N = 0. Then we have:
m*g*cos(θ) - 0 = m*vf^2 / R
g*cos(θ) = vf^2 / R
vf^2 = R*g*cos(θ)
vf^2 = 1.45*32.2*cos(34)
vf^2 = 38.708 ft/s
- Using conservation of energy for initial release point and point where sphere leaves cylinder:
ΔK.E = ΔP.E
0.5*m* ( vf^2 - vi^2 ) = m*g*(R - R*cos(θ))
( vf^2 - vi^2 ) = 2*g*R*( 1 - cos(θ))
vi^2 = vf^2 - 2*g*R*( 1 - cos(θ))
vi^2 = 38.708 - 2*32.2*1.45*(1-cos(34))
vi^2 = 22.744
vi = 4.77 ft/s
G
has the SI units
m
3
k
g
⋅
s
2
Answer:
Second order line appears at 43.33° Bragg angle.
Explanation:
When there is a scattering of x- rays from the crystal lattice and interference occurs, this is known as Bragg's law.
The Bragg's diffraction equation is :
.....(1)
Here n is order of constructive interference, λ is wavelength of x-ray beam, d is the inter spacing distance of lattice and θ is the Bragg's angle or scattering angle.
Given :
Wavelength, λ = 1.4 x 10⁻¹⁰ m
Bragg's angle, θ = 20°
Order of constructive interference, n =1
Substitute these value in equation (1).

d = 2.04 x 10⁻¹⁰ m
For second order constructive interference, let the Bragg's angle be θ₁.
Substitute 2 for n, 2.04 x 10⁻¹⁰ m for d and 1.4 x 10⁻¹⁰ m for λ in equation (1).


<em>θ₁ </em>= 43.33°
Answer: The person will still have a mass of 90kg on Mars
Explanation: The Truth is, the mass of a body remains constant from place to place. It is the weight which is equal to {mass of body * acceleration due to gravity{g}} that varies from place to place since it is dependent on {g}.
In this case the person will have a Weight of 90*9.8 = 882N on Earth.
{ "g" on Earth is 9.8m/s²}
And a Weight of 90*3.3 = 297N on Mars.
{ From the question "g" on Mars is {9.8m/s²}/3 which is 3.3m/s²}
From this analysis you notice that the WEIGHT of the person Varies but the MASS remained Constant at 90kg.