Ball and a spring#

I have built a game that involves a spring, a smooth slope, and a little ball of \(m = \)0.4 kg. The slope is 26\(^{\circ}\) above the horizontal. The spring is placed into a small hole such that when it is compressed to the proper starting position, and the ball is placed upon it, the ball will be at the height \(h = \)0 m. The spring has been compressed by 3 cm and has a spring constant of \(k = \)600 N/m.

Part 1#

When I press a button, the ball is pushed up the slope by the spring. How fast is the ball traveling when it is 0.05 m up the slope?

Answer Section#

Please enter in a numeric value in \( m{m/s}\).

Part 2#

How fast is the ball traveling when it is 0.1 m up the slope?

Answer Section#

Please enter in a numeric value in \( m{m/s}\).

Part 3#

What is the maximum DISTANCE the ball reaches from the bottom of the slope?

Answer Section#

Please enter in a numeric value in \( m{m}\).

Part 4#

Calculate the acceleration of the ball as it goes UP the slope once it is beyond the spring?

You may draw a free body diagram in order to help you write the final acceleration vector in terms of \(\hat\imath\) (pointing down-slope) and \(\hat\jmath\) (pointing perpendicular to the slope). Enter answer as a symbolic expression (sin(30) instead of 0.86602).

For

Use

\(\hat\imath\)

i_hat

\(\hat\jmath\)

j_hat

\(g\)

g

Answer Section#

Part 5#

What is the acceleration of the ball as it goes DOWN the slope? Justify your answer.

Answer Section#

Answer in the box below.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.