Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
The force exerted by the beam imparts an average acceleration with magnitude [tex]a_{\rm ave}[/tex] such that
[tex]0^2 - v^2 = -2a_{\rm ave} (0.12\,\mathrm m) \implies a_{\rm ave} = \dfrac{v^2}{0.24\,\rm m}[/tex]
where [tex]v[/tex] is the speed of the pile driver at the moment it first touches the beam.
Presumably, the pile driver is dropped from rest, so any work done on the pile driver as it falls is done exclusively by gravity. Initially, the pile driver has potential energy
[tex]P = (2100\,\mathrm{kg}) g (5.00\,\mathrm m) = 102,900 \,\rm J[/tex]
which, assuming no friction or air resistance is involved, gets totally converted to kinetic energy. Then the speed of the pile driver is such that
[tex]K = P \implies 102,900 \,\mathrm J = \dfrac12(2100\,\mathrm{kg})v^2 \implies v^2 = 98\dfrac{\rm m^2}{\rm s^2}[/tex]
and so the average acceleration of the pile driver as it comes to a stop has magnitude
[tex]a_{\rm ave} = \dfrac{98\frac{\rm m}{\rm s}}{0.24\,\rm m} \approx 408\dfrac{\rm m}{\rm s^2}[/tex]
Hence the beam exerts an average force of magnitude
[tex]F_{\rm ave} = (2100\,\mathrm{kg}) a_{\rm ave} = 857,500\,\mathrm N \approx \boxed{858\,\mathrm{kN}}[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.