A ball with a mass of #640 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #36 (kg)/s^2# and was compressed by #5/8 m# when the ball was released. How high will the ball go?

Answer 1

The height is #=1.12m#

The spring constant is #k=36kgs^-2#

The compression is #x=5/8m#

The potential energy is

#PE=1/2*36*(5/8)^2=7.03J#

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

#KE=1/2m u^2#

The initial velocity is #=u#

#u^2=2/m*KE=2/m*PE#

#u^2=2/0.64*7.03=21.97#

#u=sqrt21.97=4.69ms^-1#

Resolving in the vertical direction #uarr^+#

We apply the equation of motion

#v^2=u^2+2ah#

At the greatest height, #v=0#

and #a=-g#

So,

#0=21.97-2*9.8*h#

#h=21.97/(2*9.8)=1.12m#

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Answer 2

To find the maximum height reached by the ball, use the principle of conservation of mechanical energy. The initial mechanical energy stored in the spring is equal to the potential energy of the ball at its maximum height.

  1. Calculate the potential energy stored in the spring using the formula ( PE_{\text{spring}} = \frac{1}{2} k x^2 ), where ( k ) is the spring constant and ( x ) is the compression of the spring.
  2. Convert the mass of the ball to kilograms.
  3. Use the formula for gravitational potential energy ( PE_{\text{gravity}} = mgh ) to find the maximum height ( h ).
  4. Set the potential energy stored in the spring equal to the gravitational potential energy and solve for ( h ).

[ PE_{\text{spring}} = \frac{1}{2} k x^2 ] [ PE_{\text{gravity}} = mgh ]

After solving for ( h ), you can find the maximum height the ball will reach.

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Answer from HIX Tutor

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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