Statics Tutorial
ENGR 210 - Statics Tutorial 1 Your Name: Partner’s Names:
Section:_____________ _______________________ _________________ _________________ _________________ _________________ _________________ _________________ VECTORS
This assignment will introduce the use of the Cartesian Coordinate System, vector notation, and properties of vectors to find corresponding unit vectors and resultant forces. The dot product will also be introduced. Each group will choose the origin of a coordinate system in the room and will identify two points on the walls. These points will be labeled A and B. Working with these points, provide answers to the following in both S.I. and U.S. Customary units (where possible): 1) Estimate the distance between the two points without making any measurements.
2)
Describe the two points in vector form by measuring their positions in Cartesian coordinates.
3)
Compute the displacement vector pointing from A to B utilizing the coordinates in 2).
4)
Measure the distance between the two points directly by using the measuring devices provided and compare with above result. Calculate the distance between the points and compare with 4).
5)
6)
Compute the unit vector pointing from A to B.
7)
If the tension in a string stretched between points A and B is 5 lb., what is the force that the string exerts on the second point? Express your answer in vector form.
Use the following definition of the dot product for the last problem: ! ! ! ! ! ! ! ! For any vectors U and V , U • V = U V cos θ where θ is the angle between U and V .
8) a. Calculate the magnitudes of the position vectors in 2) and 3).
b.
Determine the angle between the vector from the origin to point A and the displacement vector from 3) by using the dot product definition.
c.
Measure this angle using the protractor provided and compare with the result of 8b).
Section:_____________ _______________________ _________________ _________________ _________________ _________________ _________________ _________________ VECTORS
This assignment will introduce the use of the Cartesian Coordinate System, vector notation, and properties of vectors to find corresponding unit vectors and resultant forces. The dot product will also be introduced. Each group will choose the origin of a coordinate system in the room and will identify two points on the walls. These points will be labeled A and B. Working with these points, provide answers to the following in both S.I. and U.S. Customary units (where possible): 1) Estimate the distance between the two points without making any measurements.
2)
Describe the two points in vector form by measuring their positions in Cartesian coordinates.
3)
Compute the displacement vector pointing from A to B utilizing the coordinates in 2).
4)
Measure the distance between the two points directly by using the measuring devices provided and compare with above result. Calculate the distance between the points and compare with 4).
5)
6)
Compute the unit vector pointing from A to B.
7)
If the tension in a string stretched between points A and B is 5 lb., what is the force that the string exerts on the second point? Express your answer in vector form.
Use the following definition of the dot product for the last problem: ! ! ! ! ! ! ! ! For any vectors U and V , U • V = U V cos θ where θ is the angle between U and V .
8) a. Calculate the magnitudes of the position vectors in 2) and 3).
b.
Determine the angle between the vector from the origin to point A and the displacement vector from 3) by using the dot product definition.
c.
Measure this angle using the protractor provided and compare with the result of 8b).