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A car of mass m = 1100 kg is traveling down a θ = 14 degree incline. When the car's speed is v0 = 13 m/s, a mechanical failure causes all four of its brakes to lock. The coefficient of kinetic friction between the tires and road is μk = 0.45. Calculate the distance the car travels down the hill L in meters until it comes to a stop at the end

A car of mass m = 1100 kg is traveling down a θ = 14 degree incline. When the car's speed is v0 = 13 m/s, a mechanical failure causes all four of its brakes to lock. The coefficient of kinetic friction between the tires and road is μk = 0.45. Calculate the distance the car travels down the hill L in meters until it comes to a stop at the end

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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A car of mass m = 1100 kg is traveling down a θ = 14 degree incline. When the car's speed is v0 = 13 m/s, a mechanical failure causes all four of its brakes to lock. The coefficient of kinetic friction between the tires and road is μk = 0.45.

Calculate the distance the car travels down the hill L in meters until it comes to a stop at the end

### Motion on an Inclined Plane #### Description This diagram illustrates a block at the top of an incline, initially at rest, but it is about to begin moving down the inclined plane with an initial velocity \( v_0 \). The incline makes an angle \( \theta \) with the horizontal axis. #### Components of the Diagram - **Block**: Represented as a square object, located at the top of the incline. It has an initial velocity \( v_0 \), depicted by a black arrow pointing down the slope. - **Inclined Plane**: Shown in blue, the plane is tilted at an angle \( \theta \) from the horizontal ground, facilitating the block’s acceleration downwards due to gravity. - **Coordinate Axes**: The diagram includes perpendicular axes labeled \( x \) and \( y \): - **Horizontal Axis (x)**: Depicts the ground level. - **Vertical Axis (y)**: Represents the height. #### Key Points - **Initial Velocity (\( v_0 \))**: The initial speed at which the block starts its motion down the plane. - **Angle of Incline (\(\theta\))**: The angle between the inclined plane and the horizontal ground. This angle is crucial in determining the components of gravitational force acting on the block. #### Concept Explanation: When a block slides down an incline, its motion can be analyzed by decomposing the gravitational force into two components: one parallel to the incline (causing the block to accelerate downwards) and one perpendicular to the incline (counteracted by the normal force). This diagram serves as an essential visual aid for understanding the motions and forces in play when dealing with objects on inclined planes in physics.
Transcribed Image Text:### Motion on an Inclined Plane #### Description This diagram illustrates a block at the top of an incline, initially at rest, but it is about to begin moving down the inclined plane with an initial velocity \( v_0 \). The incline makes an angle \( \theta \) with the horizontal axis. #### Components of the Diagram - **Block**: Represented as a square object, located at the top of the incline. It has an initial velocity \( v_0 \), depicted by a black arrow pointing down the slope. - **Inclined Plane**: Shown in blue, the plane is tilted at an angle \( \theta \) from the horizontal ground, facilitating the block’s acceleration downwards due to gravity. - **Coordinate Axes**: The diagram includes perpendicular axes labeled \( x \) and \( y \): - **Horizontal Axis (x)**: Depicts the ground level. - **Vertical Axis (y)**: Represents the height. #### Key Points - **Initial Velocity (\( v_0 \))**: The initial speed at which the block starts its motion down the plane. - **Angle of Incline (\(\theta\))**: The angle between the inclined plane and the horizontal ground. This angle is crucial in determining the components of gravitational force acting on the block. #### Concept Explanation: When a block slides down an incline, its motion can be analyzed by decomposing the gravitational force into two components: one parallel to the incline (causing the block to accelerate downwards) and one perpendicular to the incline (counteracted by the normal force). This diagram serves as an essential visual aid for understanding the motions and forces in play when dealing with objects on inclined planes in physics.
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