What should you do immediately if a boat motor catches fire?
1 answer:
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Answer:
Time period of horizontal Oscillation = T = 2
As you can see, from the equation, Period of oscillation depends upon the mass and the spring constant. Not on the displacement.
Explanation:
Solution:
As we know that:
F = Kx
Here,
K = Spring constant
x = displacement.
First, they are displacing it with 6 cm from its rest position for which Time period of the oscillation is T = 2 seconds.
But next, they want to know the effect on the time period of the oscillation if the displacement x is doubled from 6cm to 12 cm.
First of all, let us see the equation of the time period of the oscillation.
We need to check, if time period does depend on the displacement or not.
As we know,
Time period of horizontal Oscillation = T = 2
As you can see, from the equation, Period of oscillation depends upon the mass and the spring constant. Not on the displacement.
Since, K is the constant for a particular spring, we need to change the mass of the cart to change the time period.
Hence the Time period will remain same.
Answer:
The answer to the question is
The roller coaster will reach point B with a speed of 14.72 m/s
Explanation:
Considering both kinetic energy KE = 1/2×m×v² and potential energy PE = m×g×h
Where m = mass
g = acceleration due to gravity = 9.81 m/s²
h = starting height of the roller coaster
we have the given variables
h₁ = 36 m,
h₂ = 13 m,
h₃ = 30 m
v₁ = 1.00 m/s
Total energy at point 1 = 0.5·m·v₁² + m·g·h₁
= 0.5 m×1² + m×9.81×36
=353.66·m
Total energy at point 2 = 0.5·m·v₂² + m·g·h₂
= 0.5×m×v₂² + 9.81 × 13 × m = 0.5·m·v₂² + 127.53·m
The total energy at 1 and 2 are not equal due to the frictional force which must be considered
Total energy at point 2 = Total energy at point 1 + work done against friction
Friction work = F×d×cosθ = ( × mg)×60×cos 180 = -117.72m
0.5·m·v₂² + 127.53·m = 353.66·m -117.72m
0.5·m·v₂² = 108.41×m
v₂² = 216.82
v₂ = 14.72 m/s
The roller coaster will reach point B with a speed of 14.72 m/s