Answer:
the work required for the loading of second dart is 64 times greater as work required for loading the first dart.
Explanation:
k = spring constant of the spring loaded toy dart gun
x₁ = compression of spring to load the first dart = d
x₂ = compression of spring to load the second dart = 8 d
E₁ = Work required to load the first dart
E₂ = Work required to load the second dart
Work required to load the first dart is given as
E₁ = (0.5) k x₁² = (0.5) k d²
Work required to load the second dart is given as
E₂ = (0.5) k x₂² = (0.5) k (8d)² = (64) (0.5) k d²
E₂ = 64 E₁
So the work required for the loading of second dart is 64 times greater as work required for loading the first dart
The balloon was 30.65 meters above ground.
ANSWER: A
The answer is 18000 J
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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
Answer:
Final volumen first process 
Final Pressure second process 
Explanation:
Using the Ideal Gases Law yoy have for pressure:

where:
P is the pressure, in Pa
n is the nuber of moles of gas
R is the universal gas constant: 8,314 J/mol K
T is the temperature in Kelvin
V is the volumen in cubic meters
Given that the amount of material is constant in the process:

In an isobaric process the pressure is constant so:



Replacing : 

Replacing on the ideal gases formula the pressure at this piont is:

For Temperature the ideal gases formula is:

For the second process you have that
So:



