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Horizontal escape lanes made of loose gravel have been constructed at the side of some roads on steep hills so that vehicles can stop safely when their brakes fail - AQA - A-Level Physics - Question 1 - 2018 - Paper 1
Question 1
Horizontal escape lanes made of loose gravel have been constructed at the side of some roads on steep hills so that vehicles can stop safely when their brakes fail. ... show full transcript
Worked Solution & Example Answer:Horizontal escape lanes made of loose gravel have been constructed at the side of some roads on steep hills so that vehicles can stop safely when their brakes fail - AQA - A-Level Physics - Question 1 - 2018 - Paper 1
Step 1
Determine the force decelerating the vehicle 2.0 s after entering the escape lane.
Answer
To determine the force exerted on the vehicle, we first need to find its deceleration. From the graph, at 2.0 seconds, the speed of the vehicle is approximately 15 m/s. At 0 seconds, it would begin from an assumed speed (approximately 20 m/s).
We can use the formula for acceleration
a = rac{ ext{change in speed}}{ ext{time}} = rac{15 ext{ m/s} - 20 ext{ m/s}}{2 ext{ s}} = -2.5 ext{ m/s}^2.
Next, using Newton's second law, the force can be calculated as follows:
F = m imes a = 1.8 imes 10^4 ext{ kg} imes (-2.5 ext{ m/s}^2) = -45,000 ext{ N}.
The negative sign indicates that the force is acting in the opposite direction of the motion.
Step 2
Deduce whether a lane of length 85 m is long enough to stop the vehicle, assuming that the engineer's graph is correct.
Answer
To determine if 85 m is sufficient, we first need to calculate the stopping distance. Using the equation:
d = rac{v^2}{2a},
where v = 20 m/s and a = 2.5 m/s²:
d = rac{(20 ext{ m/s})^2}{2 imes 2.5 ext{ m/s}^2} = rac{400}{5} = 80 ext{ m}.
Since 80 m < 85 m, the lane is indeed long enough to stop the vehicle.
Step 3
Discuss the energy transfers that take place when a vehicle is decelerated in an escape lane.
Answer
When a vehicle decelerates in an escape lane, the kinetic energy (KE) of the vehicle is converted into other forms of energy. The primary energy transfer occurs as follows:
- The kinetic energy of the vehicle is transferred into heat energy due to friction between the vehicle's tires and the gravel. This heat increases the temperature of the gravel.
- Some energy may also be transferred to the ground as potential energy changes if there is an incline in the lane. Consequently, the vehicle loses its kinetic energy and comes to rest.
Step 4
Deduce whether this escape ramp is sufficient to stop the vehicle.
Answer
To find out if the ramp is sufficient, we calculate the vertical height change using trigonometry:
The ramp length is 85 m and it makes an angle of 25° with the horizontal. The height (h) can be calculated as:
\approx 85 ext{ m} imes 0.4226 = 35.9 ext{ m}.$$ Using the height to determine if this ramp can stop the vehicle: The kinetic energy before entering the ramp: $$KE = rac{1}{2}mv^2 = rac{1}{2} imes 1.8 imes 10^4 ext{ kg} imes (20 ext{ m/s})^2 \ = 3.6 imes 10^6 ext{ J}.$$ The potential energy gained when ascending this height: $$PE = mgh = (1.8 imes 10^4 ext{ kg}) imes (9.81 ext{ m/s}^2) imes (35.9 ext{ m}) \ o = 6.4 imes 10^6 ext{ J}.$$ Since KE > PE, the ramp is sufficient to stop the vehicle.Step 5
Discuss whether an escape lane containing gravel or an escape ramp would provide the safer experience for the driver of the vehicle as it comes to rest.
Answer
Using gravel as an escape lane allows for a controlled deceleration, absorbing the energy from the vehicle gradually through friction. It prevents the driver from experiencing a sudden stop, which can be safer in terms of avoiding injury. However, gravel can be unpredictable under certain conditions, such as when wet.
On the other hand, an escape ramp, if appropriately designed like an upward slope with a smooth surface, can also provide a safe stopping experience by converting kinetic energy into potential energy. A steeper ramp might pose greater risks of the vehicle rolling backwards if the brakes fail to engage effectively.
In conclusion, while both options can be safe under specific conditions, proper design and maintenance of the escape ramp would generally provide a safer experience compared to gravel.