Answer:
a) 17 N
b) 21 N
Explanation:
At the 3 o'clock position, the sum of the forces towards the center is:
∑F = ma
T = m v² / r
19 = m v² / r
At the 12 o'clock position, the sum of the forces towards the center is:
∑F = ma
T + mg = m v² / r
T + (0.18)(9.8) = 19
T = 17.2 N
At the 6 o'clock position, the sum of the forces towards the center is:
∑F = ma
T − mg = m v² / r
T − (0.18)(9.8) = 19
T = 20.8 N
Rounding to two significant figures, the tensions are 17 N and 21 N.
C because the stack of paper was divided into 4
Answer:
What is the intensity is 1.3349 × 10⁻⁷ w/m²
Explanation:
Given that;
λ = 582 nm = 582 × 10⁻⁹
R = 75.0 cm = 0.75 m
d = 0.640 mm = 0.000640 m
a = 0.434 mm = 0.000434 m
I₀ = 4.40×10⁻⁴ W/m²
y = 0.710 mm = 0.00071 m
Now to get our tanФ we say
tanФ = y/R = 0.00071 / 0.75 = 0.0009466
Ф is so small
∴ tanФ ≈ sinФ
So
∅ = 2πdsinФ / λ
we substitute
∅ = ( 2π × 0.000640 × 0.0009466 ) / 582 × 10⁻⁹
= 6.54 rad
Now
β = 2πasinФ / λ
we substitute
β = ( 2π × 0.000434 × 0.0009466 ) / 582 × 10⁻⁹
β = 4.435 rad
I = I₀ cos²(∅/2) [(sin(β/2))/(β/2)]²
we substitute
I = 4.40×10⁻⁴ cos(3.27)² [ (sin(2.2175)) / (2.2175) ]²
= 4.40×10⁻⁴ × 0.9967 × 0.0003044
= 1.3349 × 10⁻⁷ w/m²
Answer:
Part A) the angular acceleration is α= 44.347 rad/s²
Part B) the angular velocity is 195.13 rad/s
Part C) the angular velocity is 345.913 rad/s
Part D ) the time is t= 7.652 s
Explanation:
Part A) since angular acceleration is related with angular acceleration through:
α = a/R = 10.2 m/s² / 0.23 m = 44.347 rad/s²
Part B) since angular acceleration is related
since
v = v0 + a*(t-t0) = 51.0 m/s + (-10.2 m/s²)*(3.4 s - 2.8 s) = 44.88 m/s
since
ω = v/R = 44.88 m/s/ 0.230 m = 195.13 rad/s
Part C) at t=0
v = v0 + a*(t-t0) = 51.0 m/s + (-10.2 m/s²)*(0 s - 2.8 s) = 79.56 m/s
ω = v/R = 79.56 m/s/ 0.230 m = 345.913 rad/s
Part D ) since the radial acceleration is related with the velocity through
ar = v² / R → v= √(R * ar) = √(0.23 m * 9.81 m/s²)= 1.5 m/s
therefore
v = v0 + a*(t-t0) → t =(v - v0) /a + t0 = ( 1.5 m/s - 51.0 m/s) / (-10.2 m/s²) + 2.8 s = 7.652 s
t= 7.652 s