Given a friction force of 1.10 N, how fast is a 0.510 kg book moving in 0.50 s if it starts at rest and you are applying a force
1 answer:
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Answer:
884 balloons
Explanation:
Assume ideal gas, since temperature is constant, then the product of pressure and volume is constant.
So if pressures reduces from 100 to 1.2, the new volume would be
The spherical volume of each of the balloon of 30cm diameter (15 cm or 0.15 m in radius) is
The number of balloons that 12.5 m3 can fill in is
Answer:
q = q₀ sin (wt)
Explanation:
In your statement it is not clear the type of circuit you are referring to, there are two possibilities.
1) The circuit of this problem is a system formed by an Ac voltage source and a capacitor, in this case all the voltage of the source is equal to the voltage at the terminals of the capacitor
ΔV = Δ
we assume that the source has a voltage of the form
ΔV = ΔV₀o sin wt
The capacitance of a capacitor is
C = q / ΔV
q = C ΔV sin wt
the current in the circuit is
i = dq / dt
i = c ΔV₀ w cos wt
if we use
cos wt = sin (wt + π / 2)
we make this change by being a resonant oscillation
we substitute
i = w C ΔV₀ sin (wt + π/2)
With this answer we see that the current in capacitor has a phase factor of π/2 with respect to the current
2) Another possible circuit is an LC circuit.
In this case the voltage alternates between the inductor and the capacitor
V_{L} + V_{C} = 0
L di / dt + q / C = 0
the current is
i = dq / dt
they ask us for a solution so that
L d²q / dt² + 1 / C q = 0
d²q / dt² + 1 / LC q = 0
this is a quadratic differential equation with solution of the form
q = A sin (wt + Ф)
to find the constant we derive the proposed solution and enter it into the equation
di / dt = Aw cos (wt + Ф)
d²i / dt²= - A w² sin (wt + Ф)
- A w² + 1 /LC A = 0
w = √ (1 / LC)
To find the phase factor, for this we use the initial conditions for t = 0
in the case of condensate for t = or the charge is zero
0 = A sin Ф
Ф = 0
q = q₀ sin (wt)
1)
The force of gravitation between the two objects is given by:
where
is the gravitational constant
m1 = 20,000 kg is the mass of the first object
m2 = 12,500 kg is the mass of the second object
r = 5 m is the distance between the two objects
Substituting the numbers inside the equation, we find
2)
From the formula in exercise 1), we see that the force is inversely proportional to the square of the distance:
this means that if we cut in a half the distance without changing the masses, the magnitude of the forces changes by a factor
So, the gravitational force increases by a factor 4. Therefore, the new force will be
3) 12.5 Nm
The torque is equal to the product between the magnitude of the perpendicular force and the distance between the point of application of the force and the centre of rotation:
Where, in this case:
F = 25 N is the perpendicular force
d = 0.5 m is the distance between the force and the center
By using the equation, we find
4) 0.049 kg m^2/s
The relationship between angular momentum (L), moment of inertia (I) and angular velocity () is:
In this problem, we have
So, the angular momentum is