Question
Asked Oct 14, 2019
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In the figure, a runaway truck with failed brakes is moving downgrade at 107 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of θ = 20°. The truck's mass is 1.4 × 104 kg. (a) What minimum length L must the ramp have if the truck is to stop (momentarily) along it? (Assume the truck is a particle, and justify that assumption.) Does the minimum length L increase, decrease, or remain the same if (b) the truck’s mass is decreased and (c) its speed is decreased?

L
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L

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Expert Answer

Step 1

Given,

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m 1.4x10 Kg 0=20° u-107 Km/h 29.72 m/sec

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Step 2

To solve such problem, we need to apply Conservation of Energy,

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ΔΕ0 ΑΚΕ+ ΔΡΕ 0

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Step 3

If we assume that Potential Energy (PE) of truck is zero at height H then at top of ramp velocity of truck will be maximum so Kinetic Energy (KE) of truck is maximum. While moving downwards...

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KE, PE 1 -тu? %3D mgh 2 By fig. of ramp, h=Lsin 1 - mu = mgLsin 2 L = 2g sin (i)

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