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Introduction to Engineering Design: Projectile Motion and Spring Stiffness, Exercises of Engineering

Montgomery CollegeEngineering

A series of exercises designed to introduce students to fundamental engineering concepts, including projectile motion, spring stiffness, and data analysis. It guides students through calculations, data visualization, and interpretation using spreadsheet software. The exercises cover topics such as determining the trajectory of a projectile, calculating the velocity of a falling object, and analyzing the relationship between force and displacement in a spring.

Typology: Exercises

2023/2024

Uploaded on 10/28/2024

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Introduction to Engineering Design ENES100
HW#1
Due: Sept 17th, 2024
Name:
M#:
1. When an object is launched from the ground with an initial velocity of V0 at an angle of θ, the
horizontal and vertical displacements of the object travel before it hits ground can be written as functions
of time t :
The object was launched with the initial
velocity 15 m/s with the angle 30o from
the ground. Use g = 9.81 m/s2.
1. Construct a spreadsheet to calculate the horizontal and vertical displacements of the ball for time t ranging
from 0 to 1.52 seconds in increments of 0.02 sec. Name your worksheet as “Analysis”.
2. Plot the functions X and Y verse time t (i.e. X-t and Y-t graphs) on a same graph.
3. Plot the trajectory of the baseball (ie. Y v.s. X graph).
4. Using the graph and your data to determine the maximum height reached by the ball and the horizontal
distances it travels before it strikes the ground. Insert comments on the cells that have maximum height and
the longest distance it travels.
5. Print your spreadsheet results with comment from 4) and charts from 2) and 3).
6. If the initial velocity changes to 20 m/s and the tossing angle changes from 30o to 45o, what will be the
maximum height reached by the ball? When will the ball hit the ground? Use time increment 0.04 sec. Adjust
your numbers in the analysis worksheet accordingly (maybe you need to add more time in your time t too,
since it will take longer time for the ball to reach the ground). Print your worksheet.
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Download Introduction to Engineering Design: Projectile Motion and Spring Stiffness and more Exercises Engineering in PDF only on Docsity!

Introduction to Engineering Design ENES

HW# 1

Due: Sept 17 th, 202 4 Name: M#:

  1. When an object is launched from the ground with an initial velocity of V0 at an angle of θ, the horizontal and vertical displacements of the object travel before it hits ground can be written as functions of time t :

The object was launched with the initial velocity 15 m/s with the angle 30o from the ground. Use g = 9.81 m/s2.

  1. Construct a spreadsheet to calculate the horizontal and vertical displacements of the ball for time t ranging from 0 to 1.52 seconds in increments of 0.02 sec. Name your worksheet as “Analysis”.
  2. Plot the functions X and Y verse time t (i.e. X-t and Y-t graphs) on a same graph.
  3. Plot the trajectory of the baseball (ie. Y v.s. X graph).
  4. Using the graph and your data to determine the maximum height reached by the ball and the horizontal distances it travels before it strikes the ground. Insert comments on the cells that have maximum height and the longest distance it travels.
  5. Print your spreadsheet results with comment from 4) and charts from 2) and 3).
  6. If the initial velocity changes to 20 m/s and the tossing angle changes from 30o to 45o, what will be the maximum height reached by the ball? When will the ball hit the ground? Use time increment 0.04 sec. Adjust your numbers in the analysis worksheet accordingly (maybe you need to add more time in your time t too, since it will take longer time for the ball to reach the ground). Print your worksheet.
  1. A construction worker accidentally drops a brick from the top of a 170 meters building. Use Excel to answer the following questions:

a. What is the velocity of the brick after 4.0 s? b. How far does the brick fall during this time? c. What will be the velocity just before hitting the ground? d. Make a plot of time and vertical velocity

  1. You hang a basketball attached to a strong string from the ceiling. At every 10 cm on the string, make a mark on the string. Then you start swinging the basketball back and forth and measure the time it takes to complete a complete swing (this is called the Period (T)). You change the length of the string according to the data below and measure the period at different lengths, see data below. All lengths are in cm and the time in seconds. s

Is there a relationship between the length of the string and the period of each swing? If yes, find the relationship using excel. if not, explain your answer.

What do you think the period would be for a lenght equal to 185 cm?

  1. A baseball has been tossed with the initial velocity 15 m/s with the angle 30 degrees from the ground. Use g = 9. m/s2. Construct a spreadsheet to calculate the horizontal and vertical displacements of the ball for time t ranging from 0 to 1.52 seconds in increments of 0.02 sec using the following equations:

X(t) = V0 t cos (θ) Y(t)=V0 tsin(θ)–1/2gt

  1. Plot the functions X and Y verse time t (i.e. X-t and Y-t graphs) on a same graph.
  2. Plot the trajectory of the baseball (ie. Y v.s. X graph).
  3. What is the highest altitude the ball reaches?
  4. How far in the horizontal distance does the ball reaches?
  5. At what angle, approximately, would I need to throw the ball to double the highest altitude? Explain how you ob- tained your answer.
  6. If the initial velocity changes to 20 m/s and the tossing angle changes from 30o to 45o, what will be the maximum height reached by the ball? When will the ball hit the ground? Use time increment 0.04 sec. Adjust your numbers in the analysis worksheet accordingly (maybe you need to add more time in your time t too, since it will take longer time for the ball to reach the ground). Print your worksheet.