A ball with a mass of #420 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #35 (kg)/s^2# and was compressed by #9/6 m# when the ball was released. How high will the ball go?
The height gained by the ball is
When the ball is projected vertically, it acquires a new potential energy, while the spring acquires the compression energy because of it's compression.
m is mass of ball, g is acceleration due to gravity, h is height gained by the ball, k is spring constant, x is compression of the spring.
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To find the maximum height the ball reaches, you can use the conservation of mechanical energy. The initial mechanical energy (when the spring is compressed) equals the final mechanical energy (when the ball is at its highest point).
Initial mechanical energy (Ei) = Potential energy stored in the spring = 1/2 * k * x^2 Final mechanical energy (Ef) = Potential energy at maximum height = m * g * h
Setting Ei equal to Ef, we have:
1/2 * k * x^2 = m * g * h
Rearranging for h:
h = (1/2 * k * x^2) / (m * g)
Substitute the given values:
h = (1/2 * 35 * (9/6)^2) / (0.42 * 9.8) h = 0.5625 meters
Therefore, the ball will go approximately 0.5625 meters high.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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