Math Problem Statement

A block of mass π‘š = 25 π‘˜π‘” is sliding at an initial velocity 𝑣 . It 0 = 10 π‘š/𝑠 experiences a pushing force measured in Newtons and given by the equation 𝑃 = 10π‘₯ starting at a position x=0. The block is pushed along a surface with 2

  • 2 coefficients of friction Β΅ and . 𝑠 = 0. 80 Β΅ π‘˜ = 0. 25 a. Find the work done by the pushing force while the block is pushed in a straight line from x = 0 m to x = 5.0 m. b. Find the work done by friction while the block is pushed in a straight line from x = 0 m to x = 5.0 m. c. Find the speed of the block when it is at the position x = 5.0 m

Solution

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Math Problem Analysis

Mathematical Concepts

Physics
Work-Energy Theorem
Kinetics
Integration in Calculus

Formulas

Work done by a variable force W = ∫ F(x) dx
Kinetic friction force F_k = ΞΌ_k * m * g
Work-Energy Theorem: Ξ”KE = Work_net

Theorems

Work-Energy Theorem

Suitable Grade Level

Undergraduate Level (Physics I or equivalent)