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A robot pushes a 20-kg box on the horizontal surface as part of the moving job. The force is 300 N to the left shown, and the box is moving. The coefficients of friction between the floor and box are us = 0.75 and uk = 0.40. What is the acceleration of the box, in m/s²? Use g = 10 m/s2. (Hint: what is the net force?) Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.

A robot pushes a 20-kg box on the horizontal surface as part of the moving job. The force is 300 N to the left shown, and the box is moving. The coefficients of friction between the floor and box are us = 0.75 and uk = 0.40. What is the acceleration of the box, in m/s²? Use g = 10 m/s2. (Hint: what is the net force?) Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.

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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**Problem Statement:** A robot pushes a 20-kg box on the horizontal surface as part of the moving job, the force is 35 N to the left shown. The box does not move. The coefficients of friction between the floor and box are μₛ = 0.75 and μₖ = 0.40. What is the magnitude of the friction force on the box, in Newtons? Use g = 10 m/s². **Instructions:** - Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. **Explanation:** The image accompanying the text shows an illustration of an orange robot pushing a large wooden box on a horizontal surface. Behind the robot and box, there is a background of mountains and grass, and the robot is depicted as making an effort to push the box to the left. **Answer:** 1. Calculate the normal force (N) acting on the box: \[ N = mg \] \[ N = 20 \text{ kg} \times 10 \text{ m/s}^2 \] \[ N = 200 \text{ N} \] 2. Calculate the maximum static friction force (fₛ): \[ fₛ = μₛ \times N \] \[ fₛ = 0.75 \times 200 \text{ N} \] \[ fₛ = 150 \text{ N} \] 3. Since the applied force (35 N) is less than the maximum static friction force (150 N), the box does not move and the static friction force equals the applied force. **Final Answer:** \[ \boxed{35} \] This friction force prevents the box from moving and balances the applied force.
Transcribed Image Text:**Problem Statement:** A robot pushes a 20-kg box on the horizontal surface as part of the moving job, the force is 35 N to the left shown. The box does not move. The coefficients of friction between the floor and box are μₛ = 0.75 and μₖ = 0.40. What is the magnitude of the friction force on the box, in Newtons? Use g = 10 m/s². **Instructions:** - Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. **Explanation:** The image accompanying the text shows an illustration of an orange robot pushing a large wooden box on a horizontal surface. Behind the robot and box, there is a background of mountains and grass, and the robot is depicted as making an effort to push the box to the left. **Answer:** 1. Calculate the normal force (N) acting on the box: \[ N = mg \] \[ N = 20 \text{ kg} \times 10 \text{ m/s}^2 \] \[ N = 200 \text{ N} \] 2. Calculate the maximum static friction force (fₛ): \[ fₛ = μₛ \times N \] \[ fₛ = 0.75 \times 200 \text{ N} \] \[ fₛ = 150 \text{ N} \] 3. Since the applied force (35 N) is less than the maximum static friction force (150 N), the box does not move and the static friction force equals the applied force. **Final Answer:** \[ \boxed{35} \] This friction force prevents the box from moving and balances the applied force.
**Text Transcription for Educational Website:** --- ### Problem Statement A robot pushes a 20-kg box on the horizontal surface as part of the moving job. The force is 300 N to the left shown, and the box is moving. The coefficients of friction between the floor and box are μₛ = 0.75 and μₖ = 0.40. What is the acceleration of the box, in m/s²? Use g = 10 m/s². (Hint: what is the net force?) **Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.** --- #### Image Description The image depicts a robot pushing a box across a horizontal surface. The robot is illustrated in an orange color, bent slightly forward, with its arms extended to apply force to the left side of the box. The box appears as a large, brown wooden crate. The background includes a simple graphical representation of mountains and a blue sky.
Transcribed Image Text:**Text Transcription for Educational Website:** --- ### Problem Statement A robot pushes a 20-kg box on the horizontal surface as part of the moving job. The force is 300 N to the left shown, and the box is moving. The coefficients of friction between the floor and box are μₛ = 0.75 and μₖ = 0.40. What is the acceleration of the box, in m/s²? Use g = 10 m/s². (Hint: what is the net force?) **Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.** --- #### Image Description The image depicts a robot pushing a box across a horizontal surface. The robot is illustrated in an orange color, bent slightly forward, with its arms extended to apply force to the left side of the box. The box appears as a large, brown wooden crate. The background includes a simple graphical representation of mountains and a blue sky.
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