### Problem DescriptionTwo people are pulling a heavy 95 kg box across the floor as shown in the figure. Person A is pulling in the x-direction only with a force of 20 N. Person B is pulling at an angle \( \theta = 40^\circ \) above the x-direction, also with a force of 20 N. What is the total pulling force on the box in the x-direction?#### Diagram Explanation:The diagram includes:- A blue rectangular box which represents the 95 kg box.- Two arrows indicating the direction and magnitude of the forces: - \( F_A \) which is a horizontal arrow pointing to the right. This represents the 20 N force applied by Person A. - \( F_B \) which is an arrow pointing above and to the right. This represents the 20 N force applied by Person B at an angle of \( 40^\circ \) to the horizontal.- The angle \( \theta \) of \( 40^\circ \) between \( F_B \) and the horizontal x-direction is marked.### Options for the Total Pulling Force in the x-Direction:- \( \) 23 N- \( \) 35 N- \( \) 45 N- \( \) 40 N### Solution:To calculate the total pulling force on the box in the x-direction, we must break down the forces into their components along the x-direction (horizontal):- The force \( F_A \) is already in the x-direction: \[ F_A = 20 \text{ N} \]- The force \( F_B \) has a horizontal (x-direction) component and a vertical component. We only need the horizontal component. Using trigonometry, the x-component of \( F_B \) is: \[ F_{Bx} = F_B \cos(\theta) = 20 \cos(40^\circ) \approx 20 \times 0.766 = 15.32 \text{ N} \]Adding the x-components together:\[ F_{\text{total, x}} = F_A + F_{Bx} = 20 \text{ N} + 15.32 \text{ N} = 35.32 \text{ N} \approx 35 \text{ N} \]### Answer:\( 35 \text{ N} \)

Answered: Image /qna-images/answer/cecd409f-d34c-4869-a7d0-cd4fcf868bbc.jpg

Two people are pulling a heavy 95 kg box across the floor as shown in the figure. Person A is pulling in the x-direction only with a force of 20 N. Person B is pulling at an angle e = 40° above the x-direction, also with a force of 20 N. What is the total pulling force on the box in the x-direction?

Two people are pulling a heavy 95 kg box across the floor as shown in the figure. Person A is pulling in the x-direction only with a force of 20 N. Person B is pulling at an angle e = 40° above the x-direction, also with a force of 20 N. What is the total pulling force on the box in the x-direction?

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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