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To solve this problem we will apply the principle of conservation of energy. For this purpose, potential energy is equivalent to kinetic energy, and this clearly depends on the position of the body. In turn, we also note that the height traveled is twice that of the rigid rod, therefore applying these concepts we will have
Therefore the minimum speed at the bottom is required to make the ball go over the top of the circle is 4.67m/s
The spring constant is 181.0 N/m
Explanation:
We can solve the problem by applying the law of conservation of energy. In fact, the elastic potential energy initially stored in the compressed spring is completely converted into gravitational potential energy of the dart when the dart is at its maximum height. Therefore, we can write:
where the term on the left represents the elastic potential energy of the spring while the term on the right is the gravitational potential energy of the dart at maximum height, and where
k is the spring constant of the spring
x = 2.08 cm = 0.0208 m is the compression of the spring
m = 12.3 g = 0.00123 kg is the mass of the dart
is the acceleration due to gravity
h = 3.25 m is the maximum height of the dart
Solving for k, we find:
Learn more about potential energy:
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