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A 3kg block slides along a floor with coefficient of kinetic friction lk = 0.3, initially moving at 7.0m/s. It travels for 2.0 meters, then encounters a ramp sloped upward at 40°. The ramp also has a coefficient of kinetic friction lk = 0.3. How fast is the block moving when it reaches the bottom of the ramp? How far up the ramp does the block slide, before momentarily coming to rest?

A 3kg block slides along a floor with coefficient of kinetic friction lk = 0.3, initially moving at 7.0m/s. It travels for 2.0 meters, then encounters a ramp sloped upward at 40°. The ramp also has a coefficient of kinetic friction lk = 0.3. How fast is the block moving when it reaches the bottom of the ramp? How far up the ramp does the block slide, before momentarily coming to rest?

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
Section: Chapter Questions
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**A 3 kg block slides along a floor with a coefficient of kinetic friction \( \mu_k = 0.3 \), initially moving at 7.0 m/s. It travels for 2.0 meters, then encounters a ramp sloped upward at 40°. The ramp also has a coefficient of kinetic friction \( \mu_k = 0.3 \). How fast is the block moving when it reaches the bottom of the ramp? How far up the ramp does the block slide, before momentarily coming to rest?** **Explanation of Problem Context:** - **Initial Setup:** A block with a mass of 3 kg is initially moving on a horizontal surface. - **Coefficient of Friction:** Both the initial surface and the ramp have the same coefficient of kinetic friction, \( \mu_k = 0.3 \). - **Initial Speed:** The block starts with a velocity of 7.0 m/s. - **Travel Distance on Horizontal Surface:** The block travels 2.0 meters before reaching the ramp. - **Ramp Incline:** The ramp is inclined at an angle of 40°. **Problem Objectives:** 1. **Determine the Speed at the Bottom of the Ramp:** - Calculate the speed of the block as it reaches the bottom of the ramp after overcoming friction on the horizontal surface. 2. **Calculate Distance Up the Ramp:** - Determine how far the block travels up the ramp before coming to a momentary stop due to the gravitational and frictional forces acting against its motion. **Note:** - This problem involves concepts of mechanics, including kinetic friction, Newton's laws of motion, and energy conservation. - Solving the problem will require applying physics principles such as work done by friction, gravitational components on an incline, and energy transformation.
Transcribed Image Text:**A 3 kg block slides along a floor with a coefficient of kinetic friction \( \mu_k = 0.3 \), initially moving at 7.0 m/s. It travels for 2.0 meters, then encounters a ramp sloped upward at 40°. The ramp also has a coefficient of kinetic friction \( \mu_k = 0.3 \). How fast is the block moving when it reaches the bottom of the ramp? How far up the ramp does the block slide, before momentarily coming to rest?** **Explanation of Problem Context:** - **Initial Setup:** A block with a mass of 3 kg is initially moving on a horizontal surface. - **Coefficient of Friction:** Both the initial surface and the ramp have the same coefficient of kinetic friction, \( \mu_k = 0.3 \). - **Initial Speed:** The block starts with a velocity of 7.0 m/s. - **Travel Distance on Horizontal Surface:** The block travels 2.0 meters before reaching the ramp. - **Ramp Incline:** The ramp is inclined at an angle of 40°. **Problem Objectives:** 1. **Determine the Speed at the Bottom of the Ramp:** - Calculate the speed of the block as it reaches the bottom of the ramp after overcoming friction on the horizontal surface. 2. **Calculate Distance Up the Ramp:** - Determine how far the block travels up the ramp before coming to a momentary stop due to the gravitational and frictional forces acting against its motion. **Note:** - This problem involves concepts of mechanics, including kinetic friction, Newton's laws of motion, and energy conservation. - Solving the problem will require applying physics principles such as work done by friction, gravitational components on an incline, and energy transformation.
1) Draw a pictorial representation of the problem. 2) Choose two coordinate systems, one for the flat surface part of the problem, one for the ramp part of the problem. 3) List given information as consistent with your chosen coordinates. Be sure to choose variable names that are not ambiguous (for example, do not use vₓ for final velocity in both parts.
Transcribed Image Text:1) Draw a pictorial representation of the problem. 2) Choose two coordinate systems, one for the flat surface part of the problem, one for the ramp part of the problem. 3) List given information as consistent with your chosen coordinates. Be sure to choose variable names that are not ambiguous (for example, do not use vₓ for final velocity in both parts.
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