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In a nutshell, a smaller rock is propelled into the air as a huge counterweight in the back falls down, effectively converting gravitational potential energy into kinetic energy for the rock and the weight. But, since the rock is smaller it is propelled at a much faster velocity! Let's say we wanted to hurl a 50 kg boulder at a castle wall 100 meters away. Our wooden structure for the trebuchet is 10 meters tall, so that is the maximum distance the counterweight can fall. Assuming the launch angle is a perfect 45 degrees, and the boulder is released from ground level, derive the needed mass of the counterweight that will give the boulder enough kinetic energy to reach the base of the castle walls. You may assune no energy is "lost" due to friction, and ALL the counterweight's gravitational potential energy is converted into the boulder's kinetic energy (HINT: You will need to employ 2D kinematics to find the needed final velocity, then use that final velocity in an energy equation to get to the mass of the counterweight.)

In a nutshell, a smaller rock is propelled into the air as a huge counterweight in the back falls down, effectively converting gravitational potential energy into kinetic energy for the rock and the weight. But, since the rock is smaller it is propelled at a much faster velocity! Let's say we wanted to hurl a 50 kg boulder at a castle wall 100 meters away. Our wooden structure for the trebuchet is 10 meters tall, so that is the maximum distance the counterweight can fall. Assuming the launch angle is a perfect 45 degrees, and the boulder is released from ground level, derive the needed mass of the counterweight that will give the boulder enough kinetic energy to reach the base of the castle walls. You may assune no energy is "lost" due to friction, and ALL the counterweight's gravitational potential energy is converted into the boulder's kinetic energy (HINT: You will need to employ 2D kinematics to find the needed final velocity, then use that final velocity in an energy equation to get to the mass of the counterweight.)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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In a nutshell, a smaller rock is propelled into the air as a huge counterweight in the back falls down, effectively converting gravitational potential energy into kinetic energy for the rock and the weight. But, since the rock is smaller, it is propelled at a much faster velocity! Let's say we wanted to hurl a 50 kg boulder at a castle wall 100 meters away. Our wooden structure for the trebuchet is 10 meters tall, so that is the maximum distance the counterweight can fall. Assuming the launch angle is a perfect 45 degrees, and the boulder is released from ground level, derive the needed mass of the counterweight that will give the boulder enough kinetic energy to reach the base of the castle walls. You may assume no energy is "lost" due to friction, and ALL the counterweight's gravitational potential energy is converted into the boulder's kinetic energy. (HINT: You will need to employ 2D kinematics to find the needed final velocity, then use that final velocity in an energy equation to get to the mass of the counterweight.) - 325 kg - 500 kg - 250 kg - 400 kg
Transcribed Image Text:In a nutshell, a smaller rock is propelled into the air as a huge counterweight in the back falls down, effectively converting gravitational potential energy into kinetic energy for the rock and the weight. But, since the rock is smaller, it is propelled at a much faster velocity! Let's say we wanted to hurl a 50 kg boulder at a castle wall 100 meters away. Our wooden structure for the trebuchet is 10 meters tall, so that is the maximum distance the counterweight can fall. Assuming the launch angle is a perfect 45 degrees, and the boulder is released from ground level, derive the needed mass of the counterweight that will give the boulder enough kinetic energy to reach the base of the castle walls. You may assume no energy is "lost" due to friction, and ALL the counterweight's gravitational potential energy is converted into the boulder's kinetic energy. (HINT: You will need to employ 2D kinematics to find the needed final velocity, then use that final velocity in an energy equation to get to the mass of the counterweight.) - 325 kg - 500 kg - 250 kg - 400 kg
Expert Solution
Step 1

GIVEN:

*Mass of boulder is 50 kg

*Castle wall 100 m away

*Height of trebuchet is 10 m 

*Launch angle is 45°

TO FIND:

*To find the mass of counterweight

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