Goal of Problem
Set #1: This assignment is meant to help
you understand:
- the quantities of motion-position,
velocity, acceleration, mass, and force,
- the differences between speed, velocity,
and acceleration,
- what weight is and how it differs
from mass,
- about work and energy,
- about rotational motion,
- and about friction.
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| The Segway Human Transporter or "HT" is
a unique, two-wheeled vehicle that carries a single, standing passenger
at speeds up to 12.5 mph. While its methods of steering, control, and
balance are a bit too complicated for us at this point, much of its basic
physics is already within our reach.
For now, all you need to know about the
Segway HT is that you stand on a platform between two forward-facing
wheels, one to the left of your feet and one to the right. When you
lean forward, the two wheels spin forward and the platform drives forward.
When you lean backward, the two wheels spin backward and the platform
drives backward. And when you turn a steering control, the two wheels
spin at different rates or in different directions and the platform
pivots so that you face a new direction. For more on the Segway HT,
you can watch videos of it in action at http://www.segway.com/video/
or visit the Segway web site at www.segway.com.
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1. You step onto the platform of
the HT and stand there motionless. While you remain still, (A)
what forces (if any) are acting on you and (B) what is the
net force on you?
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2. You lean forward and the HT begins
to pick up speed in the forward direction. During this period time,
(A) are you accelerating and, if so, in which direction and
(B) do you have a velocity and, if so, in which direction?
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3. The HT reaches full speed and
you begin to ride it up a smooth, uniform ramp. As you ride
straight ahead up this ramp at full speed,
what are (A) your acceleration, (B) your velocity, (C)
the net force you are experiencing, and (D) the force your
feet are exerting on the platform of the HT?
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4. The ramp is 3 meters high and
its paved surface is 50 meters long. As you and the HT climb this
ramp, (A) is one of you (your body
and the HT) doing work on the other? (B) If so,
which one and how much overall work does that one do on the other?
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5. You return to level pavement
and then stop briefly to pick up your extraordinarily heavy backpack.
When you start the HT moving forward, you notice that it is now struggling
to pick up speed. (A) What aspect of the backpack is affecting
the HT's ability to pick up speed and (B) why?
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6. You finally reach your friend's
home and slow to a stop. As you and the HT are stopping,
but are not yet stopped, in which direction are (A)
the net force on you, if any, (B) your acceleration, if any,
and (C) your velocity, if any?
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7. As you and the HT come to a stop,
but are not yet stopped, what type(s) of force does the
pavement exert on the HT and in which direction(s)?
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8. To impress your friend, you keep
the HT in one place but pivot the device rapidly around and around.
You begin by (a) pivoting clockwise (as viewed from above)
as fast as possible, then (b) reverse directions, and finish
by (c) pivoting counterclockwise as fast as possible. During
which time or times (a, b, or c) do you (A) have the
largest amount of angular velocity, (B) have the largest amount
of angular acceleration, (C) experience the largest amount
of torque, and (D) have the largest moment of inertia (assume
that you remain rigid throughout this stunt)?
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