**Practice:**1. A force **F** with \(\vec{F} = 8\hat{i} - 3\hat{j} \, \text{N}\) acts on a particle that undergoes a displacement from point A with \(x, y\) coordinates \((1 \, \text{m}, 0 \, \text{m})\) to point B with coordinates \((2 \, \text{m}, -2 \, \text{m})\). a) What is the work done by the force?---**Solution:**To find the work done by the force \(\vec{F}\), we use the dot product of the force vector and the displacement vector.First, determine the displacement vector \(\vec{d}\):\[\vec{d} = (2 \, \text{m} - 1 \, \text{m})\hat{i} + (-2 \, \text{m} - 0 \, \text{m})\hat{j} = \hat{i} - 2\hat{j}\]Next, find the dot product of \(\vec{F}\) and \(\vec{d}\):\[\vec{F} = 8\hat{i} - 3\hat{j}\]\[\vec{d} = 1\hat{i} - 2\hat{j}\]\[\vec{F} \cdot \vec{d} = (8\hat{i} - 3\hat{j}) \cdot (1\hat{i} - 2\hat{j})\]\[= 8\hat{i} \cdot 1\hat{i} + 8\hat{i} \cdot (-2\hat{j}) - 3\hat{j} \cdot 1\hat{i} - 3\hat{j} \cdot (-2\hat{j})\]\[= 8 \cdot 1 + 8 \cdot 0 - 3 \cdot 0 - 3 \cdot (-2)\]\[= 8 + 6\]\[= 14 \, \text{J}\]So, the work done by the force is ### Physics Problems on Motion and Friction#### Problem Set:1. **Particle Speed Calculation** - **Question:** b) What is the speed of the particle at point B if its speed at point A is 3.00 m/s and its mass is 0.50 kg?2. **Object Sliding Down an Inclined Plane** - **Given Data:** - Mass of the object, \( m = 5.00 \, \text{kg} \) - Initial height of the object, \( h = 2.00 \, \text{m} \) - Initial speed of the object, \( v_0 = 0.50 \, \text{m/s} \) - **Questions:** a) If there is no friction, what is the speed of the object when it reaches the bottom of the inclined plane? b) If there is friction with a coefficient of \(\mu = 0.20\) and the angle of the inclined plane is \(30^\circ\), what is the speed of the object when it reaches the bottom?3. **Object Attached to Vertical Spring** - **Given Data:** - Mass of the object, \( m = 5.00 \, \text{kg} \) - Spring constant, \( k = 100 \, \text{N/m} \) - Displacement from initial position, \( x = 20.0 \, \text{cm} \) (or \( 0.20 \, \text{m} \)) - **Question:** What is the speed of the object when it has fallen 20.0 cm from its original position?#### Explanation of Concepts:- **Speed Calculation at Different Points:** Calculations often use principles of conservation of energy and kinematics equations to find the final speed of objects.- **Impact of Friction:** Understanding how frictional forces impact the motion of objects on inclined planes, involving calculations of frictional force and its impact on net acceleration and final speed.- **Spring-Mass Systems:** Use concepts of potential energy in springs (Hooke’s Law) and gravitational potential energy to determine the speed at a given displacement.#### Diagrams and Graphs**Note:**This document did not contain any diagrams or graphs, but for an educational website, including

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Enoitzoq isnigh ai Practice: 1. A force F with arrow = 81-31 N acts on a particle that undergoes a displacement from point A with x, y coordinates (1 m, 0m) to point B with coordinates (2m, -2m). a) What is the work done by the force?

Enoitzoq isnigh ai Practice: 1. A force F with arrow = 81-31 N acts on a particle that undergoes a displacement from point A with x, y coordinates (1 m, 0m) to point B with coordinates (2m, -2m). a) What is the work done by the force?

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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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