Curvilinear Motion of a crate carried by a crane

Curvilinear Motion of a crate carried by a crane#

A crane moves a crate through point A with a speed of \({{ params.v_0 }}\ \rm{m/s}\) and increases the speed constantly at a rate of \({{ params.a }}\ \rm{m/s^{2}}\).
Find the magnitude of the crate’s acceleration when the arc length is \({{ params.s }}\ \rm{m}\) and when \(x_0 =0 \ \rm{m}\).
The equation of the arc is \(y= m - \frac{x^{2}}{w}\)
\(w = {{ params.w }}\ \rm{m}\), \(m = {{ params.m }}\ \rm{m}\)

../../../../../_images/crane.png

Part 1#

Find the speed \(v_2\) when \(x = 0\ \rm{m}\).

Answer Section#

Please enter the speed in \(m/s\).

Part 2#

Find the radius of curvature.

Answer Section#

Please enter the radius in \(m\).

Part 3#

Find \(a_n\) at the same point.

Answer Section#

Please enter the acceleration in \(m/s^{2}\).

Part 4#

Find the total acceleration.

Answer Section#

Please enter the acceleration in \(m/s^{2}\).

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.