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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.

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Answer

To find the force, we first need to establish the deceleration. Using the graph at 2.0 s, the speed is approximately 10 m/s. The initial speed can be taken as the speed at 0 s, which is around 20 m/s.

Using the formula for acceleration: $a = \frac{v_f - v_i}{t}$

where:

$v_f$ (final velocity) = 10 m/s
$v_i$ (initial velocity) = 20 m/s
$t$ (time) = 2 s

We find: $a = \frac{10 - 20}{2} = -5 \text{ m/s}^2$

Now, using Newton's second law: $F = m \cdot a$

where:

$m = 1.8 \times 10^4$ kg
$a = -5 \text{ m/s}^2$

Thus: $F = 1.8 \times 10^4 \cdot (-5) = -9.0 \times 10^4 \, \text{N}$

The force decelerating the vehicle is $9.0 \times 10^4 \, \text{N}$ in the opposite direction of 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.

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Answer

To determine if an 85 m lane is sufficient, we need to calculate the distance required to stop the vehicle. Using the formula for distance under uniform acceleration: $d = v_i t + \frac{1}{2} a t^2$

Where:

$v_i = 20 \, \text{m/s}$ (initial speed)
$a = -5 \, \text{m/s}^2$ (deceleration)
$t = 2 \, \text{s}$ (time taken to stop)

Calculating: $d = 20 \cdot 2 + \frac{1}{2} \cdot (-5) \cdot (2)^2$ $d = 40 - 10 = 30 \, \text{m}$

Thus, for the vehicle to stop is 30 m, an 85 m lane is sufficient to stop the vehicle.

Step 3

Discuss the energy transfers that take place when a vehicle is decelerated in an escape lane.

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Answer

When a vehicle is decelerated, its kinetic energy is converted to other forms of energy. Initially, the vehicle possesses kinetic energy given by: $KE = \frac{1}{2} mv^2$

As the vehicle decelerates, this kinetic energy is transformed primarily into:

Heat Energy: Through friction between the tires and the gravel, generating heat.
Potential Energy: If in a sloped escape lane, the vehicle's energy may convert to gravitational potential energy as it climbs.
Sound Energy: From the noise of tires against gravel, dissipating energy into the environment.

This energy transformation illustrates the conservation of energy principle.

Step 4

Deduce whether this escape ramp is sufficient to stop the vehicle.

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Answer

Calculate the deceleration and stopping distance for the ramp scenario. First, determine the vertical height using trigonometry: $h = 85 \cdot \sin(25^") \approx 35.4 \, \text{m}$

Apply the same stopping distance formula: Using:

$v_i = 20 \, \text{m/s}$
Assume similar deceleration as gravel, say $-5 \, \text{m/s}^2$ (idealized)

Distance required to stop: $d_{ramp} = 20 \cdot 2 + \frac{1}{2} \cdot (-5) \cdot (2^2) = 30 \, \text{m}$

Since $85 \, \text{m} > 30 \, \text{m}$ , 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.

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Answer

An escape lane with gravel generally offers better traction, but may lead to longer stopping distances compared to a ramp. The ramp, however, allows for controlled deceleration while utilizing gravitational potential energy effectively.

In terms of safety:

Gravel: Increases risk due to potential for skidding but offers higher stopping power.
Ramp: Aids in effective deceleration, but requires precise angle and surface quality to minimize slipping.

Overall, while both can be effective, a well-designed ramp could offer a more controlled and potentially safer experience compared to gravel.

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

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

Determine the force decelerating the vehicle 2.0 s after entering the escape lane.

Deduce whether a lane of length 85 m is long enough to stop the vehicle, assuming that the engineer's graph is correct.

Discuss the energy transfers that take place when a vehicle is decelerated in an escape lane.

Deduce whether this escape ramp is sufficient to stop the vehicle.

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.

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