Friday 20 January 2012
Class meeting
Topics
Textbook sections
Ponderables
Mini-labs (deliv.)
Lab
Demonstrations
Mini-lectures
Quiz
Other
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PHYS 116 SCALE-UP
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Vectors
Chap. 3
Inclined Plane
Vectors (whiteboards)
Rear-end collision
Mini-lab: Vectors (70 min)
o Equipment: for each group: whiteboard, meter stick, protractor
Ponderable (25 min): Inclined Plane
Quiz (15 min): Rear-end collision
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Friday 20 January 2012
PHYS 116 SCALE-UP
VECTORS
In this activity you will explore various ways of combining vectors. You will need these skills later in the
semester to manipulate the vectors that represent different physics quantities.
Pre-lab: Consider two vectors with these components: A  17iˆ  23 ˆj  9kˆ and B  5iˆ  11 ˆj  3kˆ
Determine the x, y and z coordinates of the vectors C  A  B , D  B  A , and E  A  B .
Determine the magnitude of the scalar product F  A  B .
Explorations
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Vector addition
Use a ruler to construct a coordinate system and then draw an
arbitrary vector R0 on the whiteboard. Make sure to leave
enough room for all four quadrants. Put the tail of the vector on
the origin (see figure to right). This vector represents the position
of an object with respect to the origin.
o
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Draw a second vector R  V0t , different than R0 . Find its components. V0 is the object’s
velocity and t represents time.
Add the components of vectors R0 and DR to find the components of R , where R = R0 + DR .
o
Draw R .
Graphically add R0 + DR and compare the result to that from your component addition.
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Repeat for R0 - DR .
Interpret the physical meaning of the vectors R , R0 , and DR .
o
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Find the coordinates of the head of the vector. What are
the x and y components of the vector, R0x and R0y?
Measure the length and the angle, from the x-axis, of the
vector. Calculate the components using trigonometry and
compare to those measured above.
Vector dot product
Consider new vectors F and d . F represents a force and d represents a displacement (the distance
over which the force is applied). Their scalar (or “dot”) product F  d  Fxd x  Fyd y represents the
work done by the force during the displacement—we will consider this quantity in Chapter 7. Calculate
the components of your vectors F and d numerically. From this result, calculate cos  , where  is the
angle between F and d . Measure  and compare the value to your calculation.
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Friday 20 January 2012
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PHYS 116 SCALE-UP
Vector cross product
Return to the vectors d and F . Find the vector  1 such that 1  d  F with the formula 1  dF sin  ,
and the right hand rule.  1 represents the torque exerted by the force F applied at a displacement d
from the axis—we will consider torque in Chapter 10. What plane is vector  1 perpendicular to? Find
t 2 = F ´d and compare it to t 1 = d ´ F . Does the cross product commute (i.e.is  1   2 ?) Vectors d
and F can be interpreted as 2 adjacent sides of a parallelogram. Approximate the area of the
parallelogram by any means you prefer, and confirm that the magnitude of the vector cross product
t 1 = d ´ F is equal to this area.
Deliverable: You will photograph your whiteboards and upload the photos to the class Sakai site as the
deliverable for this lab.
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Friday 20 January 2012
PHYS 116 SCALE-UP
INCLINED PLANE
The inclined plane is one of the most important physics models in the analysis of vector
kinematics. The figure shows an inclined plane with two vector forces: gravity, denoted by Fg ,
and a normal force, denoted by N . An acceleration is also denoted by a .
Also shown in the figure are two possible coordinate systems, denoted by (x1, y1) and (x2, y2)
The task is to write the components of N , a , and Fg in each of the two coordinate systems, as a
function of the angle q .
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Friday 20 January 2012
PHYS 116 SCALE-UP
QUIZ #2
Tony is happily speeding down a two-lane road in his old, orange Datsun going 80 km/h when he
suddenly realizes he is about to rear-end the brand-new, bright-red sports car that has stopped in front
of him. He sees that in the car is his best friend, Andy.
a. If Tony is 50 m away when he hits the brakes, what constant acceleration is needed to avoid a
rear-end collision?
b.
If when Tony first sees Andy’s car it is not stopped, but instead is moving at 60 km/h, what
would be the maximum speed Tony can have just as he reaches Andy’s car if he is not to rearend it?
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