Mechanics Problems - Force and Linear
Kinematics Problems
Note: Each problem begins with a list of forces
necessary to solve the context-rich problem. These are for the
benefit of the instructor. Delete the list before using the
problems in your class.
- Weight, Normal: While driving in the mountains, you
notice that when the freeway goes steeply down hill,
there are emergency exits every few miles. These
emergency exits are straight dirt ramps which leave the
freeway and are sloped uphill. They are designed to stop
trucks and cars that lose their breaks on the downhill
stretches of the freeway even if the road is covered in
ice. You are curious, so you stop at the next emergency
road. You estimate that the road rises at an angle of 10o
from the horizontal and is about 100 yards (300 ft) long.
What is the maximum speed of a truck that you are sure
will be stopped by this road, even if the frictional
force of the road surface is negligible?
- Weight, Normal: While driving in the mountains, you
notice that when the freeway goes steeply down hill,
there are emergency exits every few miles. These
emergency exits are straight dirt ramps which leave the
freeway and are sloped uphill. They are designed to stop
trucks and cars that lose their breaks on the downhill
stretches of the freeway even if the road is covered in
ice. You wonder at what angle from the horizontal an
emergency exit should rise to stop a 50 ton truck going
70 mph up a ramp 100 yards (300 ft) long, even if the
frictional force of the road surface is negligible.
- Weight, Normal: You have opened a small delivery business that
guarantees to deliver any box between 5 lbs. and 500 lbs. to any
location in the area by the next day. At your distribution center, boxes
slide down a ramp between the delivery and the sorting area. You must
determine the angle this ramp should have so that a box will take 5.0
seconds to slide down the ramp when starting from rest at the top. When
the box arrives at the bottom of the ramp, you decide that its speed
should be no larger than 10 ft/s so as not to damage the contents of the
box. Using the latest technology, the surface of the ramp will be
extremely slippery.
- Weight, Normal: You are watching a ski jump contest on
television when you wonder how high the skier is when she
leaves the starting gate. In the ski jump, the skier
glides down a long ramp. At the end of the ramp, the
skier glides along a short horizontal section which ends
abruptly so that the skier goes into the air. You
measured that the skier was in the air for 2.3 seconds
and landed 87 meters, in the horizontal direction, from
the point she went into the air. Make the best estimate
of the height of the starting gate at the top of the ramp
from the horizontal section from which the skier takes
off into the air. Make clear on what assumptions your
answer depends (this is why it is an estimate).
- Weight, Normal, Friction: You are passing a construction
site on the way to physics class, and stop to watch for
awhile. The construction workers appear to be going on
coffee break, and have left a large concrete block
resting at the top of a wooden ramp. As soon as their
backs are turned, the block begins to slide down the
ramp. You quickly clock the time for the block to reach
the bottom of the ramp at 10 seconds. You wonder how long
the ramp is. You estimate that the ramp is at an angle of
about 20o to the horizontal. In your physics book you
find that the coefficient of kinetic friction between
concrete and wood is 0.35.
- Weight, Normal, Friction: You have a summer job at a
company that specializes in the design of sports
facilities. The company has been given the contract to
design a new hockey rink to try to keep the North Stars
in town. The rink floor is very flat and horizontal and
covered with a thick coat of ice. Your task is to
determine the refrigeration requirements which gives best
temperature for the ice. You have a table which gives the
coefficient of static and kinetic friction between ice
and the standard NHL hockey puck as a function of ice
temperature. You have been told that the hockey game will
be more exciting if passes are swift and sure. Experts
say that the passing game is best if, after it goes 5.0
m, a puck has a speed which is 90% of the speed with
which it left the hockey stick. A puck typically has a
speed of 20 km/hr when it leaves the hockey stick for a
pass.
- Weight, Normal, Friction: You and some friends visit the
Minnesota State Fair and decide to play a game on the
Midway. To play the game you must slide a metal
hockey-type puck up a wooden ramp so that it drops
through a hole at the top of the ramp. Your prize, if you
win, is a large, pink, and rather gaudy, stuffed poodle.
You realize the secret to winning is giving the puck just
enough velocity at the bottom of the ramp to make it to
the hole. You estimate the distance from the bottom of
the ramp to the hole at about 10 feet, and the ramp
appears to be inclined with an angle of 10o from the
horizontal. You just got out of physics class and recall
the coefficient of static friction between steel and wood
is 0.1 and the coefficient of kinetic friction between
steel and wood is 0.08. The mass of the puck is about 2.5
lbs. You decide to impress your friends by sliding the
puck at the precise speed on the first try so as to land
it in the hole. You slide the puck at 8.0 ft/sec. Do you
win the stuffed poodle?
- Weight, Normal, Tension, Friction: Finally you are
leaving Minneapolis to get a few days of Spring break,
but your car breaks down in the middle of nowhere. A tow
truck weighing 4000 lbs comes along and agrees to tow
your car, which weighs 2000 lbs, to the nearest town. The
driver of the truck attaches his cable to your car at an
angle of 20o to the horizontal. He tells you that his
cable has a strength of 500 lbs. He plans to take 10
seconds to tow your car at a constant acceleration from
rest in a straight line along the flat road until he
reaches the maximum speed limit of 45 miles/hour. Can the
driver carry out his plan? You assume that rolling
friction behaves like kinetic friction, and the
coefficient of rolling friction between your tires and
the road is 0.10.
- Weight, Normal, Friction: While visiting a friend in San
Francisco you decide to drive around the city. You turn a
corner and are driving up a steep hill. Suddenly, a small
boy runs out on the street chasing a ball. You slam on
the brakes and skid to a stop leaving a 50 foot long skid
mark on the street. The boy calmly walks away but a
policeman watching from the sidewalk walks over and gives
you a ticket for speeding. You are still shaking from the
experience when he points out that the speed limit on
this street is 25 mph. After you recover your wits, you
examine the situation more closely. You determine that
the street makes an angle of 20o with the horizontal and
that the coefficient of static friction between your
tires and the street is 0.80. You also find that the
coefficient of kinetic friction between your tires and
the street is 0.60. Your car's information book tells you
that the mass of your car is 1570 kg. You weigh 130 lbs.
Witnesses say that the boy had a weight of about 60 lbs
and took 3.0 seconds to cross the 15 foot wide street.
Will you fight the ticket in court?
- Weight, Lift, Thrust, Drag: One morning while waiting for
class to begin, you are reading a newspaper article about
airplane safety. This article emphasizes the role of
metal fatigue in recent accidents. Metal fatigue results
from the flexing of airframe parts in response to the
forces on the plane especially during take off and
landings. As an example, the reporter uses a plane with a
take off weight of 200,000 lbs and take off speed of 200
mph which climbs at an angle of 30o with a constant
acceleration to reach its cruising altitude of 30,000
feet with a speed of 500 mph. The three jet engines
provide a forward thrust of 240,000 lbs by pushing air
backwards. The article then goes on to explain that a
plane can fly because the air exerts an upward force on
the wings perpendicular to their surface called
"lift." You know that air resistance is also a
very important force on a plane and is in the direction
opposite to the velocity of the plane. The article tells
you this force is called the "drag." Although
the reporter writes that some metal fatigue is primarily
caused by the lift and some by the drag, she never tells
you their size for her example plane. Luckily the article
contains enough information to calculate them, so you do.