Hills, inclement weather, and cars
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- Hills, inclement weather, and cars
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Hills, inclement weather, and cars
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[post_date] => 2025-01-09 07:31:54
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
Steep hills cause significant traffic safety problems when roads become wet or icy. The county commission office for a small town is attempting to identify the most dangerous hills in their city. They identified four roads on hills that seem to pose the most danger to drivers. Since the roads have different texture and are made of different materials, they all offer different amounts of traction between car tires and the road. The hills were tested under both icy and wet road conditions to determine the coefficients of static and kinetic friction between the road and an average car tire.
The results of the research are summarized in the table below:
Table 1. Coefficients of friction for each street at specific angles.
Trigonometric values for various angles are given below:
Table 2. Angles and their corresponding trigonometric values.
[post_title] => Hills, inclement weather, and cars
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[question] => Under icy conditions, which hill could a car park on without slipping?
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[answer] => 1
[description] => Reason for the Correct Answer:
The component of gravity acting along the ramp is mgsinθ, the force of static friction is given by μsmgcosθ
mgsinθ – μsmgcosθ = 0, so mgsinθ = μsmgcosθ or tanθ = μs
So take tanθ for each hill angle and see if the hill has the required coefficient of static friction
The only hill that has a coefficient of static friction that is larger than the required coefficient is Austin Dr since, tan(24°) = 0.445 which is less than 0.46
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[answers] => Array
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[0] => Array
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[each_answer] => A. Austin Dr
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[1] => Array
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[each_answer] => B. Pacific Ave
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[2] => Array
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[each_answer] => C. Western Ave
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[3] => Array
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[each_answer] => D. Bridger St
)
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => A 1820kg car is driving too fast up the hill on Austin Drive under icy conditions. After a deer runs across the road the driver of the car slams on the brakes, and the car skids up the hill. What is the magnitude of the acceleration of the car while it skids up the hill?
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[answer] => 1
[description] => Reason for the Correct Answer:
When the car is skidding up the hill the forces of gravity along the incline and the force of friction point in the same direction.
mgsinθ + μsmgcosθ = ma
1820kg)(9.8m/s2)sin(24°) + (0.23)(1820kg)(9.8m/s2)cos(24°) = (1820kg)a, so a = 6.0m/s2
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[answers] => Array
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[0] => Array
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[each_answer] => A. 6.0 m/s²
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[1] => Array
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[each_answer] => B. 4.7 m/s²
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[2] => Array
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[each_answer] => C. 3.5 m/s²
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[3] => Array
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[each_answer] => D. 5.3 m/s²
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => If a car is traveling fast enough and slams on the brakes it will skid regardless of whether it is moving down a hill or up a hill. Will a car experience a larger magnitude of acceleration if it skids down the Bridger St hill or up the Bridger St hill?
[value] => Array
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[answer] => 1
[description] => Reason for the Correct Answer:
Think about Newton’s Second Law ΣF=ma.
When the car is skidding down the hill the forces of gravity along the incline and the force of friction point in opposite direction.
When the car is skidding up the hill the forces of gravity along the incline and the force of friction point in the same direction.
Since both forces point in the same direction while the car is skidding up the hill, the net force will have a larger magnitude, which means the acceleration will have a larger magnitude.
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[answers] => Array
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[0] => Array
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[each_answer] => A. A car will experience more acceleration when it is skidding up Bridger St hill
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[1] => Array
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[each_answer] => B. A car will experience the same acceleration regardless if it is skidding up Bridger St hill or down Bridger St hill
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[2] => Array
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[each_answer] => C. A car will experience more acceleration when it is skidding down Bridger St hill
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[each_answer] => D. It depends on the mass of the car
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[quiz_unique_key] => 2261298308
[question] => A 2300kg car is driving down the hill on Pacific Ave after a summer rain storm. The car performs a hard brake, which causes the car to skid down the hill with its wheels locked so that they don’t rotate. What will be the acceleration of the car as it skids down Pacific Ave?
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[answer] => 3
[description] => Reason for the Correct Answer:
Use Newton’s Second Law ΣF=ma
The component of gravity acting along the ramp is mgsinθ, the force of kinetic friction is given by μkmgcosθ
mgsinθ – μkmgcosθ = ma
12,276N – 10,397N = (2300kg)a, so a = 0.82 m/s²
)
[answers] => Array
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[0] => Array
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[each_answer] => A. 1.8 m/s²
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[1] => Array
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[each_answer] => B. 0.47 m/s²
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[2] => Array
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[each_answer] => C. 0.82 m/s²
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[3] => Array
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[each_answer] => D. 1.2 m/s²
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[quiz_unique_key] => 2261298308
[question] => A 1830kg car drives down Bridger St after a rain shower and parks halfway down the hill. Two friends get out and lean on the back of the car. They debate whether their leaning on the car will cause the car to start sliding down the steep hill. What is the minimum force that the people leaning on the car would have to push with (directed along hill parallel to the road) in order to cause the car to start slipping?
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[answer] => 4
[description] => Reason for the Correct Answer:
There are now three forces exerted on the car in the direction parallel to the road.
The force from leaning plus the force of gravity would have to equal the maximum static friction while the road is wet.
F(lean) + mgsinθ – μsmgcosθ = 0, so F(lean) + (1830kg)(9.8 m/s2)sin(29°) – (0.61)(1830kg)(9.8m/s2)cos(29°)= 0, or F(lean) = 874N
)
[answers] => Array
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[0] => Array
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[each_answer] => A. 341 N
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[1] => Array
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[each_answer] => B. 1230 N
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[2] => Array
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[each_answer] => C. 1570 N
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[3] => Array
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[each_answer] => D. 874 N
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