In classical mechanics, impulse (symbolized by or Imp) is the integral of a force, , over the time interval, , for which it acts. Since force is a vector quantity, impulse is also a vector quantity. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction.
Answer: The drag force goes up by a factor of 4
Explanation:
The <u>Drag Force</u> equation is:
(1)
Where:
is the Drag Force
is the Drag coefficient, which depends on the material
is the density of the fluid where the bicycle is moving (<u>air in this case)
</u>
is the transversal area of the body or object
the bicycle's velocity
Now, if we assume , and do not change, we can rewrite (1) as:
(2)
Where groups all these coefficients.
So, if we have a new velocity , which is the double of the former velocity:
(3)
Equation (2) is written as:
(4)
Comparing (2) and (4) we can conclude<u> the Drag force is four times greater when the speed is doubled.</u>
We shall convert all of the densities to lbs/gal, so the product of
BTU/lbs and lbs/gal gives us the basis of comparison, which was "ratio of energy to volume".
grams / ml x 1 lbs/454 grams → 1 lbs/ 454 ml
1 lbs/454 ml x 3785.41 ml/gal → 3785.41 lbs/454gal
Conversion of g/ml = 8.34 lbs/gal
Looking at each fuel:
Kerosene:
18,500 x (8.34 x 0.82) = 126,517 BTU/gal
Gasoline:
20,900 x (8.34 x 0.737) = 128,463 BTU/gal
Ethanol:
11,500 x (8.34 x 0.789) = 75,673 BTU/gal
Hydrogen:
61,000 x (8.34 x 0.071) = 36,120 BTU/gal
The best fuel in terms of energy to volume ratio is Gasoline.
Gallons required:
BTU needed / BTU per gallon
= 85.2 x 10⁹ / 128,463
= 6.6 x 10⁵ gallons
Answer:
Acceleration of Object A = 0.6 m/s²
Acceleration of Object B = 0.3 m/s²
Acceleration of Object A is double than the acceleration of Object B.
Explanation:
According to the Newton's 2nd law of motion, Acceleration of an object by a net force is directly proportional to the magnitude of that net force and in the direction of that net force and inversely proportional to the mass of the object
Mathematically
F ∝ a
F = ma
Given data:
F = 15 N
m₁ = 25 kg
m₂ = 50 kg
F = m₁a₁
a₁ = F/m₁
a₁ = 15/25
a₁ = 0.6 m/s²
F = m₂a₂
a₂ = F/m₂
a₂ = 15/50
a₂ = 0.3 m/s²
It can be seen that acceleration of Object A is double than the acceleration of Object B.
Answer:
a) 1.58 kg s^{-1}
b) x_m e^{-1.58t} x_m is initial amplitude
c) 5 kg s^{-1}
Explanation:
given data:
mass =0.5 kg
k = 12.5 N/m
from the data given
a)
b)
where x_m is initial amplitude
c) critical damping amplitude