Question

# A 263-gram block is dropped on a vertical spring with a constant force a = 2.52 N / cm $Figure 20$. The block sticks to the resource, and the resource is compressed 11.8 cm before momentarily coming to rest. While the resource is being compressed, how much work is done on $a$ the force of gravity and $b$ the resource? $c$ What was the speed of the block immediately before it reached the resource? $d$ If this initial velocity of the block is doubled, what is the maximum compression of the spring?

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## Answer to a math question A 263-gram block is dropped on a vertical spring with a constant force a = 2.52 N / cm $Figure 20$. The block sticks to the resource, and the resource is compressed 11.8 cm before momentarily coming to rest. While the resource is being compressed, how much work is done on $a$ the force of gravity and $b$ the resource? $c$ What was the speed of the block immediately before it reached the resource? $d$ If this initial velocity of the block is doubled, what is the maximum compression of the spring?

Miles
4.9
$a$ \, T_g = m \times g \times h

T_g = 0.263 \, kg \times 9.8 \, m/s^2 \times 0.118 \, m = 0.304 \, J

$b$ \, T_r = -\frac{1}{2} \times k \times x^2

k = \frac{2.52 \, N/cm}{0.01 \, m/cm} = 252 \, N/m

T_r = -\frac{1}{2} \times 252 \, N/m \times $0.118 \, m$^2 = -1.756 \, J

$c$ \, T_t = T_g + T_r

= 0.304 \, J + $-1.756 \, J$ = -1.452 \, J

E_k = \frac{1}{2} \times m \times v^2

\frac{1}{2} \times 0.263 \, kg \times v^2 = 1.452 \, J

v = \sqrt{\frac{2 \times 1.452 \, J}{0.263 \, kg}} = 3.67 \, m/s

$d$ \, \text{Si se duplica la velocidad inicial, la energía cinética se cuadruplica:}

E_k = 4 \times 2.06 \, J = 8.24 \, J

E_k = \frac{1}{2} \times k \times x^2

x = \sqrt{\frac{2 \times 8.24 \, J}{252 \, N/m}} = 0.235 \, m = 23.5 \, cm

\text{Respuesta: }$a$ \, 0.304 \, J, $b$ \, -1.756 \, J, $c$ \, 3.67 \, m/s, $d$ \, 23.5 \, cm

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