In the figure, a runaway truck with failed brakes is moving downgrade at 170 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of 0 = 15°. The truck's mass is 1.5 x 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?

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem Statement:**

In the figure, a runaway truck with failed brakes is moving downgrade at 170 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of θ = 15°. The truck's mass is 1.5 × 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?

**Diagram Explanation:**

The diagram shows a truck moving up an inclined ramp. The ramp has an inclination angle θ of 15° with respect to the horizontal. The length of the ramp is labeled as L. The ramp is depicted as a frictionless surface.

**Inputs**

- (a) The number provided is 9.8 with units m/s².
  
**Choices**

- (b) The minimum length L will "remain the same" if the truck’s mass is decreased.
- (c) The minimum length L will "decrease" if the truck’s speed is decreased.
Transcribed Image Text:**Problem Statement:** In the figure, a runaway truck with failed brakes is moving downgrade at 170 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of θ = 15°. The truck's mass is 1.5 × 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? **Diagram Explanation:** The diagram shows a truck moving up an inclined ramp. The ramp has an inclination angle θ of 15° with respect to the horizontal. The length of the ramp is labeled as L. The ramp is depicted as a frictionless surface. **Inputs** - (a) The number provided is 9.8 with units m/s². **Choices** - (b) The minimum length L will "remain the same" if the truck’s mass is decreased. - (c) The minimum length L will "decrease" if the truck’s speed is decreased.
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