After coming home from class, you put your mug on a lopsided stack of textbooks, as seen
a) Draw a free body diagram on the mug.
b) If the coefficient of static friction is 0.3, the coefficient of kinetic friction is 0.25, and the
angle is 25◦
, does the mug slide and get old coffee all over your textbooks?? If so, what is
the mug’s acceleration when it slides?a
aThis is important to know in case you want to catch the mug before it spills.
You and three friends try the game depicted below.
a) Sketch a top-down view of the free body diagram for the contraption.
b) Who wins the game? The forces on the contraption are:
i) Red shirt: 30 N @ 48◦
ii) Red shorts: 42 N @ 170◦
iii) Blue shirt: 22 N @ 275◦
iv) Remaining guy: 35 N @ 353◦
Hint: think about the net force on the contraption and pick the most likely person!
In professional circuit racing, for safety reasons it is important to have the track at an angle,
as shown below.
Side view for the final turn of the Daytona International Speedway.
Top view of the Daytona International Speedway. The final turn is highlighted in red.
At the Daytona International Speedway, a car makes the final turn, as shown in red in the
“top view” figure. The radius of curvature is 280 m. Around this turn, assume the speed of
the racers is constant.
a) Draw a free body diagram for the red car in both the “side view” and “top view” figures.
Make sure you include coordinate axes!
b) The speed record at Daytona is 223 mph. How much does the track have to be angled in
order to achieve this speed around the final turn without skidding?
c) If instead the angle is 23◦
, how fast can the cars go without skidding? Make sure you answer
in miles per hour (mph).
A common hair tie can be modelled as a spring. Suppose you go for a hair tie in your
backpack and it catches on a zipper, as seen below.
a) Before you notice the hair tie is caught on the zipper, you pull with a measily 15 N of force.
The hair tie stretches 1.2 cm, but the backpack does not move. What is the spring constant
of the hair tie?
b) You realize your mistake and pull harder. The hair tie now stretches 1.6 cm and the backpack
just starts to move.a What is the force of friction on the backpack? Is it static or kinetic?
c) If your friend sits on the backpack but nothing else changes, does the force of friction change?
Why or why not? Hint: the answer is no, it does not change. The real question is: why not?
Doesn’t the frictional force depend on mass?
d) Now that your 82 kg friend is on your backpack, you really pull. The industrial-strength
hair tie now stretches to a whopping 6 cm before the bag just starts to move again. Find:
i) The coefficient of static friction between the backpack and table.
ii) The mass of the backpack.
In other words, acceleration is so small that it is negligible.
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