Answer:
The maximum speed of sonic at the bottom of the hill is equal to 19.85m/s and the spring constant of the spring is equal to (497.4xmass of sonic) N/m
Energy approach has been used to sole the problem.
The points of interest for the analysis of the problem are point 1 the top of the hill and point 2 the bottom of the hill just before hitting the spring
The maximum velocity of sonic is independent of the his mass or the geometry. It is only depends on the vertical distance involved
Explanation:
The step by step solution to the problem can be found in the attachment below. The principle of energy conservation has been applied to solve the problem. This means that if energy disappears in one form it will appear in another.
As in this problem, the potential and kinetic energy at the top of the hill were converted to only kinetic energy at the bottom of the hill. This kinetic energy too got converted into elastic potential energy .
x = compression of the spring = 0.89
This should help
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We must remember that the total net force equation at
constant velocity is:
<span>F – Ff = 0</span>
of
F - µN = 0
Using Newton's 2nd Law of Motion:<span>
F = m a
<span>Where,
F = net force acting on the body
m = mass of the body
a = acceleration of the body
Since the cart is moving at a constant velocity, then
acceleration is zero, hence the working equation simplifies to
F = net Force = 0
Therefore,
F - µN = 0
where
µ = coefficient of friction = 0.20
N = normal force acting on the cart = 12 N
Therefore,
F - 0.20(12) = 0
<span>
F = 2.4 N </span></span></span>
