# A ball with a mass of #144 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #16 (kg)/s^2# and was compressed by #6/4 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 is

This potential energy will be converted to kinetic energy when the spring is released

The initial velocity is

Resolving in the vertical direction

We apply the equation of motion

At the greatest height,

and

So,

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To determine the maximum height reached by the ball, you can use the following formula: ( H = \frac{mgh}{k} ), where ( m ) is the mass of the ball (in kg), ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 )), ( h ) is the compression of the spring (in meters), and ( k ) is the spring constant.

First, convert the mass of the ball from grams to kilograms: ( 144 , \text{g} = 0.144 , \text{kg} ).

Now, substitute the given values into the formula: ( H = \frac{(0.144 , \text{kg} \times 9.8 , \text{m/s}^2 \times (6/4) , \text{m})}{16 , \text{(kg)/s}^2} ).

Calculate the expression to find the height ( H ).

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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.

- A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- An object with a mass of #12 kg# is moving at #9 m/s# over a surface with a kinetic friction coefficient of #1 #. How much power will it take to accelerate the object at #3 m/s^2?
- How much work would it take to push a # 1 kg # weight up a # 4 m # plane that is at an incline of # (5pi) / 12 #?
- A balanced lever has two weights on it, the first with mass #6 kg # and the second with mass #8 kg#. If the first weight is # 4 m# from the fulcrum, how far is the second weight from the fulcrum?
- How much work would it take to push a # 6 kg # weight up a # 2 m # plane that is at an incline of # pi / 4 #?

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