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Physics / Fundamentals of Physics 10 / Chapter 8 / Problem 15

Fundamentals of Physics | 10th Edition | ISBN: 9781118230725 | Authors: David Halliday; Robert Resnick; Jearl Walker

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In Fig. 8-35, a runaway truck with failed brakes is moving

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QUESTION:

In Fig. 8-35, a runaway truck with failed brakes is moving downgrade at 130 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of u ! 15#.The trucks mass is 1.2 $ 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 trucks mass is decreased and (c) its speed is decreased? L Figure 8-35 15.

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QUESTION:

In Fig. 8-35, a runaway truck with failed brakes is moving downgrade at 130 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of u ! 15#.The trucks mass is 1.2 $ 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 trucks mass is decreased and (c) its speed is decreased? L Figure 8-35 15.

ANSWER:

Step 1 of 4 a) Consider is the minimum length of the ramp at which the truck finally stops. The law of conservation of energy at point A and B is given by, That is, Implies, Where is the height of the slop. We can rewrite equation one as, The initial velocity of the truck is,\n So the height of the ramp is, The height of the ramp is

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