Question

A block of mass m is dropped onto the top of a vertical spring whose force constant is k. If the block is released from a heighth above the top of the spring. a) what is the maximum energy of the block? b) What is the maximum compression of the spring? c) At what compression is the block's kinetic energy half its maximum value?​

Answer 1

Explanation:

m

is the mass of the block

k

is the spring constant

h

is the height of the block

Question A:

In this case, the maximum energy is equal to the gravitational potential energy of the block. Thus, we have:

E

m

a

x

=

m

g

h

Answer 2

Answer:

According to the law of conservation of energy, a system's initial and end total energies should be equal. In order to prevent the overall amount of energy from changing, one form of energy is simply transformed into another. That energy cannot be created or destroyed is another implication of the law.

Explanation:

• The volume of the block is m, 
• while the spring constant is k.
• The block's height is h.

[a]. Energy is constant when there is no energy loss, hence maximum energy = energy.

The potential energy is mgh wrt the upper end of the spring.

The potential energy is mg(h+x) with respect to the point of maximal compression.

The potential energy is mg(h+L) with respect to the bottom end of the spring (if L is the length of the spring).

In this instance, the greatest energy equals the gravitational potential power of the block.

$E_{max} =mgh$

[b]. Think about the spring's compression expression.

                                $mgh=\frac{1}{2} kx^{2}$

                                $x^{2} =\frac{2mgh}{k}$

                                $x=\sqrt{\frac{2mgh}{k} }$

[c]. here we have:

         $\frac{1}{2} K=\frac{1}{2} kx^{2}$

where K is the maximal energy, which corresponds to the kinetic energy.

For each variable, replace the statements.

                        $\frac{1}{2} mgh=\frac{1}{2} kx^{2}$

                         $mgh = kx^2$

                         $x=\sqrt{\frac{mgh}{k} }$

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