Answer:
(i) -556 rad/s²
(ii) 17900 revolutions
(iii) 11250 meters
(iv) -55.6 m/s²
(v) 18 seconds
Explanation:
(i) Angular acceleration is change in angular velocity over time.
α = (ω − ω₀) / t
α = (10000 − 15000) / 9
α ≈ -556 rad/s²
(ii) Constant acceleration equation:
θ = θ₀ + ω₀ t + ½ αt²
θ = 0 + (15000) (9) + ½ (-556) (9)²
θ = 112500 radians
θ ≈ 17900 revolutions
(iii) Linear displacement equals radius times angular displacement:
s = rθ
s = (0.100 m) (112500 radians)
s = 11250 meters
(iv) Linear acceleration equals radius times angular acceleration:
a = rα
a = (0.100 m) (-556 rad/s²)
a = -55.6 m/s²
(v) Angular acceleration is change in angular velocity over time.
α = (ω − ω₀) / t
-556 = (0 − 15000) / t
t = 27
t − 9 = 18 seconds
A car traveling south is 200 kilometers from its starting point after 2 hours. What is the average velocity of the car?
Choose: 100 kilometers/hour south
Answer;
=0.43 m/s²
Solution;
There will be the tension in the cable, T, upwards and the weight of the elevator, mg, downwards.
By Newton's second law, the sum of the forces will be equal to mass×acceleration.
Resultant force = m × a
Then T - mg = ma so the tension in the cable is
T = m(g+a)
The cable will break when T = 21,800 N
Solving for a, that happens when
a = 21800/2130 - g
= 10.23 - g (in m/s^2)
If you're using g = 9.8 m/s^2
Then the maximum acceleration allowed is 10.23-9.8 = 0.43 m/s^2
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Th equations to be used here are the following:
a = (v - v₀)/t
x = v₀t + 0.5at²
The speed of the fugitive is the sum of his own speed plus the speed of the train. Thus,
v₀ = 0 + 5.5 m/s = 5.5 m/s
v = 8 m/s + 5.5 m/s = 13.5 m/s
a.) We use the first equation to determine time
2.5 m/s² = (13.5 m/s - 5.5 m/s)t
Solving for t,
t = 3.2 seconds
b.) We use the answer in a) and the 2nd equation:
x = (5.5 m/s)(3.2 s) + 0.5(2.5 m/s²)(3.2 s)²
x = 30.4 meters
