For the ride to be comfortable, the magnitude of acceleration must not exceed 32 m/s2. What is the fastest constant speed that a
1 answer:
Answer:
the maximum possible constant speed is 8 m/sec
Explanation:
from the image, Given that
r(t) = (2t, t²,t²/3), -5 ≤ t ≤ 5
Given that the curvature K(t) = 2 / ( t² + 2)²
note that t² + 2 ≥ 2
(t² + 2)² ≥ 4
1 / (t² + 2)² ≤ 1/4
2 / (t² + 2)² ≤ 1/2
Also note that k(0) = 1/2
The normal component of acceleration satisfies aN = kv²
where v = ║v(t)║is the speed of the roller coaster.
The maximum possible normal component of acceleration is 32
so, aN ≤ 32 every where on the track
aN = kv² ≤ 1/2v² ≤ 32
v² ≤ 64
Therefore, the maximum possible constant speed is 8 m/sec
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When the mass of the spring changed from 0.2kg to 0.1kg, the time period changed from 1 sec to 0.5 seconds
<u>Explanation:</u>
Given-
Mass, m1 = 0.2kg
Time period, T1 = 1s
m2 = 0.1 kg
T2 = ?
We know,
where,
T = Time period
m = mass
k = spring constant
From the equation, we can see that T is directly proportion to the square root of mass, m
T ∝ √m
So,
If m1 = 0.2kg , T1 = 1s and m2 = 0.1kg
The T2 would be:
Therefore, when the mass of the spring changed from 0.2kg to 0.1kg, the time period changed from 1 sec to 0.5 seconds