Answer:
a) , b)
Explanation:
a) The Hooke's law states that spring force is directly proportional to change in length. That is to say:
In this case, the force is equal to the weight of the object:
The spring constant is:
b) The length of the spring is:
Answer:
At the lowest point in the oscillation, the momentum is zero.
At the lowest point in the oscillation,
Explanation:
Since spring block system is performing to and fro motion along straight line
So here we can say at the lowest position of its path the velocity will become zero.
So we can say that momentum of the spring block system is given as
Also we know that after reaching the lowest point the block will again go up towards its mean position
So at the lowest point of the spring block system the block will move upwards again
So this will accelerate upwards hence
The launch velocity is 4.8 m/s
Explanation:
We can solve this problem by applying the law of conservation of energy. In fact, the mechanical energy of the hopper (equal to the sum of the potential energy + the kinetic energy) is conserved. So we can write:
where:
is the initial potential energy, at the bottom
is the initial kinetic energy, at the bottom
is the final potential energy, at the top
is the final kinetic energy, at the top
We can rewrite the equation as:
where:
m is the mass of the hopper
is the acceleration of gravity
is the initial height
u is the launch speed of the hopper
is the maximum altitude reached by the hopper
v = 0 is the final speed (which is zero when the hopper reaches the maximum height)
Solving the equation for u, we find the launch speed of the hopper:
Learn more about kinetic energy and potential energy:
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