Answer:
17.6 m/s²
Explanation:
Given:
= 90 m/s (final velocity)
= 2 m/s (initial velocity)
Δt = 5s (change in time)
The formula for acceleration is:
= Δv / Δt
We can find Δv by doing
Δv = -
Replace the values
Δv = 90m/s - 2m/s
Δv= 88m/s
Using the equation from earlier, we can find the acceleration by dividing the average velocity by time.
= Δv / Δt
=
acceleration = 17.6
Answer:
The radius of the disc is 2.098 m.
(e) is correct option.
Explanation:
Given that,
Moment of inertia I = 12100 kg-m²
Mass of disc m = 5500 kg
Moment of inertia :
The moment of inertia is equal to the product of the mass and square of the radius.
The moment of inertia of the disc is given by
Where, m = mass of disc
r = radius of the disc
Put the value into the formula
Hence, The radius of the disc is 2.098 m.
Answer:
a) the required time is 0.6283 μs
b) the inductor current is 0.5 mA
Explanation:
Given the data in the question;
The capacitor voltage has its maximum value of 25 V at t = 0
i.e V = V₀ = 25 V
we determine the angular velocity;
ω = 1 / √( LC )
ω = 1 / √( ( 20 × 10⁻³ H ) × ( 8.0 × 10⁻¹² F) )
ω = 1 / √( 1.6 × 10⁻¹³ )
ω = 1 / 0.0000004
ω = 2.5 × 10⁶ s⁻¹
a) How much time does it take until the capacitor is fully discharged for the first time?
V = V₀sin( ωt )
we substitute
25V = 25V × sin( 2.5 × 10⁶ s⁻¹ × t )
25V = 25V × sin( 2.5 × 10⁶ s⁻¹ × t )
divide both sides by 25 V
sin( 2.5 × 10⁶ × t ) = 1
( 2.5 × 10⁶ × t ) = π/2
t = 1.570796 / (2.5 × 10⁶)
t = 0.6283 × 10⁻⁶ s
t = 0.6283 μs
Therefore, the required time is 0.6283 μs
b) What is the inductor current at that time?
(t) = V₀√(C/L) sin(ωt)
{ sin(ωt) = 1 )
(t) = V₀√(C/L)
we substitute
(t) = 25V × √( ( 8.0 × 10⁻¹² F ) / ( 20 × 10⁻³ H ) )
(t) = 25 × 0.00002
(t) = 0.0005 A
(t) = 0.5 mA
Therefore, the inductor current is 0.5 mA
Answer:
6.21 m/s
Explanation:
Using work energy equation then
where d is displacement from initial to final position, v is velocity and subscripts a and b are position A and B respectively, m is mass of collar, g is acceleration due to gravity
Substituting 1 Kg for m, 0.4m for h, as 0, 9.81 for g then