Answer:
It's centripetal acceleration is 301.7 m/s²
Explanation:
The formula to be used here is that of the centripetal acceleration which is
ac = rω²
where ac is the centripetal acceleration = ?
ω is the angular velocity = 3 revolutions per second is to be converted to radian per second: 3 × 2π = 3 × 2 × 3.14 = 18.84 rad/s
r is the radius = 0.85 m
ac = 0.85 × 18.84²
ac = 301.7 m/s²
It's centripetal acceleration is 301.7 m/s²
Answer:
Explanation:
The theory of propagation of error in case of addition and subtraction states that maximum errors are added in absolute terms in both the operation of addition and subtraction . So in this case the subtracted value will be
10.5775 - 10.3005
= .2770 g
errors will be added ie in subtracted value we can find error to the tune of
.0002 + .0002 = .0004 g
So the subtracted value will be written as
.2770 ± .0004
Answer:
The inductance of solenoid A is twice that of solenoid B
Explanation:
The inductance of a solenoid L is given by
L = μ₀n²Al where n = turns density, A = cross-sectional area of solenoid and l = length of solenoid.
Given that d₁ = 2d₂ and l₂ = 2l₁ and d₁ and d₂ are diameters of solenoids A and B respectively. Also, l₁ and l₂ are lengths of solenoids A and B respectively.
Since we have a cylindrical solenoid, the cross-section is a circle. So, A = πd²/4.
Let L₁ and L₂ be the inductances of solenoids A and B respectively.
So L₁ = μ₀n²A₁l₁ = μ₀n²πd₁²l₁/4
L₂ = μ₀n²A₂l₂ = μ₀n²πd₂²l₂/4
Since d₁ = 2d₂ and l₂ = 2l₁, sub
L₁/L₂ = μ₀n²πd₁²l₁/4 ÷ μ₀n²πd₂²l₂/4 = d₁²/d₂² × l₁/l₂ = (2d₂)²/d₂² × l₁/2l₁ = 4d₂²/d₂² × l₁/2l₁ = 4 × 1/2 = 2
L₁/L₂ = 2
L₁ = 2L₂
So, the inductance of solenoid A is twice that of solenoid B
Writing the acceleration as a function of time:
a(t) = 1 + 3√t
Integrating acceleration, we obtain velocity:
v(t) = t + 2(t)^(3/2) + c;
object at rest so velocity at t = 0 is 0 so c = 0.
v(t) = t + 2(t)^(3/2)
Integrating velocity to obtain an equation for displacement:
d(t) = t²/2 + 4/5 t^(5/2) + c
Applying limits from t = 0 to t = 9
d = 9²/2 + 4/5 9^(5/2)
d = 234.9 m
Answer:
The plane's acceleration is 33.33 m/s²
Explanation:
The following equation relates velocity, v and acceleration of a moving body;
v = u + a·t
Where:
v = The final velocity of the body after time, t = 180 km/min
u = The initial velocity of the body just before the counting of the time = 0 m/s
a = The acceleration of the body during time, t = Required
t = The time of the motion = 1.5 minutes = 1.5×60 seconds = 90 s
v = 180 km/min = 180 km/min × 1000 m/km × 1/60 min/s = 3000 m/s
∴ 3000 m/s = 0 m/s + a × 90
Therefore, the plane's acceleration = 33.33 m/s².
