A ball with a mass of $80 g$ $80 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $9 \frac{k g}{s^{2}}$ $9 (kg)/s^2$ and was compressed by $\frac{3}{5} m$ $3/5 m$ when the ball was released. How high will the ball go?

Question

A ball with a mass of $80 g$ $80 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $9 \frac{k g}{s^{2}}$ $9 (kg)/s^2$ and was compressed by $\frac{3}{5} m$ $3/5 m$ when the ball was released. How high will the ball go?

1 Answer

Impact of this question

1802 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-02T19:00:34

$h = \frac{81}{8} m$ $h=81/8m$

Explanation:

Given that the entire spring energy is converted to kinetic energy which later turns to potential energy.
So that means the entire spring energy is turns to potential energy
To solve, we'll use the near-earth potential equation.

Now, spring energy equation is $E = \frac{1}{2} k x^{2}$ $E=1/2kx^2$
We have, $k = 9 k \frac{g}{s^{2}}$ $k=9kg/s^2$ , $x = \frac{3}{5} m$ $x=3/5m$ . So $E = \frac{1}{2} \cdot 9 \cdot {(\frac{3}{5})}^{2}$ $E=1/2*9*(3/5)^2$
So, we end up with $E = \frac{3^{4}}{10} J$ $E=3^4/10J$

Now, The near-earth potential energy is $E = m g h$ $E=mgh$
$m = 80 g = 80 \cdot 10^{- 3} k g$ $m=80g=80*10^{-3}kg$ , $g = 10 \frac{m}{s^{2}}$ $g=10m/s^2$ , so we need to find $h$ $h$

So, equating the two, we get $3^4/cancel10^1= cancel80^8*cancel10^1*cancel10^{-3}*h$

Re-arranging gives us the answer that I have up there. You'll need a calculator to find it in decimals.

Science

Math

Humanities

... and beyond

A ball with a mass of $80 g$ $80 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $9 \frac{k g}{s^{2}}$ $9 (kg)/s^2$ and was compressed by $\frac{3}{5} m$ $3/5 m$ when the ball was released. How high will the ball go?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A ball with a mass of 80 g80g80 g is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of 9 (kg)/s^29kgs29 (kg)/s^2 and was compressed by 3/5 m35m3/5 m when the ball was released. How high will the ball go?

1 Answer

Explanation:

Related questions

Impact of this question

A ball with a mass of $80 g$ $80 g$ is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of $9 \frac{k g}{s^{2}}$ $9 (kg)/s^2$ and was compressed by $\frac{3}{5} m$ $3/5 m$ when the ball was released. How high will the ball go?