Question

When traveling through mountains, most highways periodically have emergency escape ramps to allow large, heavy vehicles to stop safely, even when their brakes are not working properly. One such escape ramp is angled 13 ∘ above the horizontal. The brakes on one large truck (mass 1.4×10⁴ kg ) fail when driving at a speed of 80 miles per hour (35.75 m/s), and the driver makes use of the escape ramp.

Part A: What is the minimum length of ramp necessary for this truck to come to a stop? Assume negligible friction and air resistance forces.

Part B: If instead dissipative forces (friction and air resistance) provide a constant force of 60,000N parallel to the ramp, what is the minimum length of ramp necessary for this truck to come to a stop?

my answer for part A is 290 m, but I am unsure how to get the answer for part B. please help

Answer 1

Part A:

Consider the truck

Net Force = Mass*Acceleration

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Use formula

Part A: ANSWER:

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Part B: With Frictional forces

Consider the truck

Net Force = Mass*Acceleration

Divide all terms by mass m

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Use formula

Part B: ANSWER:

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