A ball with a mass of #400 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #45 (kg)/s^2# and was compressed by #3/4 m# when the ball was released. How high will the ball go?
The height is
The spring constant is The compression is The potential energy in the spring is This potential energy will be converted to kinetic energy when the spring is released and to potential energy of the ball Let the height of the ball be Then , The potential energy of the ball is
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To find the maximum height the ball will reach, you can use the principle of conservation of mechanical energy. The potential energy stored in the spring when compressed is equal to the kinetic energy of the ball at its maximum height.
The potential energy stored in the spring, (PE_{spring}), is given by the formula (PE_{spring} = \frac{1}{2}kx^2), where (k) is the spring constant and (x) is the compression distance.
The kinetic energy of the ball at its maximum height, (KE_{max}), is given by (KE_{max} = mgh), where (m) is the mass of the ball, (g) is the acceleration due to gravity, and (h) is the maximum height.
Setting these two energies equal, you get:
(\frac{1}{2}kx^2 = mgh)
Solve for (h), the maximum height:
(h = \frac{x^2}{2g} )
Substitute the given values: (k = 45 , (kg)/s^2), (x = 3/4 , m), (m = 0.4 , kg), and (g = 9.8 , m/s^2).
(h = \frac{(3/4)^2}{2 \times 9.8})
(h \approx 0.0445 , m)
So, the ball will reach a maximum height of approximately 0.0445 meters.
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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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