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3) A block starts from rest. It is pushed with an applied force for d , m. It is released and travels over a rough patch. Calculate the maximum vertical displacement up the incline. m //// d,, Hx = 0 d, Hx = 0.2 d, = 10 m d2 = 3 m |F.] = 100 N m= 10 kg A = 30°

3) A block starts from rest. It is pushed with an applied force for d , m. It is released and travels over a rough patch. Calculate the maximum vertical displacement up the incline. m //// d,, Hx = 0 d, Hx = 0.2 d, = 10 m d2 = 3 m |F.] = 100 N m= 10 kg A = 30°

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
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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**Transcription and Explanation for Educational Website:** **Problem Statement:** A block starts from rest. It is pushed with an applied force for \(d_1\) meters. It is then released and travels over a rough patch. Calculate the maximum vertical displacement up the incline. **Diagram Explanation:** The diagram shows an inclined plane with an angle \(\theta\) where a block of mass \(m\) is positioned. The block is initially acted upon by an applied force \(F_a\) parallel to the incline. This force is applied over a distance \(d_1\), where the coefficient of kinetic friction \(\mu_k\) is zero, indicating a frictionless surface. After \(d_1\), the block then travels an additional distance \(d_2\) where the surface has a coefficient of kinetic friction \(\mu_k = 0.2\). **Given Parameters:** - \(d_1 = 10 \, \text{m}\) - \(d_2 = 3 \, \text{m}\) - \(|F_a| = 100 \, \text{N}\) - \(m = 10 \, \text{kg}\) - \(\theta = 30^\circ\) This problem involves calculating how far up the incline (in terms of vertical displacement) the block moves after it has been released. This involves analyzing the forces acting on the block, the work done, and the effects of friction over the rough patch.
Transcribed Image Text:**Transcription and Explanation for Educational Website:** **Problem Statement:** A block starts from rest. It is pushed with an applied force for \(d_1\) meters. It is then released and travels over a rough patch. Calculate the maximum vertical displacement up the incline. **Diagram Explanation:** The diagram shows an inclined plane with an angle \(\theta\) where a block of mass \(m\) is positioned. The block is initially acted upon by an applied force \(F_a\) parallel to the incline. This force is applied over a distance \(d_1\), where the coefficient of kinetic friction \(\mu_k\) is zero, indicating a frictionless surface. After \(d_1\), the block then travels an additional distance \(d_2\) where the surface has a coefficient of kinetic friction \(\mu_k = 0.2\). **Given Parameters:** - \(d_1 = 10 \, \text{m}\) - \(d_2 = 3 \, \text{m}\) - \(|F_a| = 100 \, \text{N}\) - \(m = 10 \, \text{kg}\) - \(\theta = 30^\circ\) This problem involves calculating how far up the incline (in terms of vertical displacement) the block moves after it has been released. This involves analyzing the forces acting on the block, the work done, and the effects of friction over the rough patch.
Expert Solution
Step 1

Calculate the work done during pushing the block.

W1=Facos30°d1=100cos30° N10 m=866 J

 

Calculate the work done by the block to cross the rough path.

W2=Facos30°-Fkd2=100cos30°-0.2×mg-Fasin30°d2=100cos30°-0.2×10×9.81-100sin30°3=230.95 J

 

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