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Exploration 3 Accelerating the cart with a different net force and constant total mass Exploration 3.1 Since the surface is very low firiction, it is possible to consider the cart and mass hanger as one system. What is the net force on the system? Explain.

Exploration 3 Accelerating the cart with a different net force and constant total mass Exploration 3.1 Since the surface is very low firiction, it is possible to consider the cart and mass hanger as one system. What is the net force on the system? Explain.

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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### Exploration 3: Accelerating the Cart with a Different Net Force and Constant Total Mass #### Exploration 3.1 **Question:** Since the surface is very low friction, it is possible to consider the cart and mass hanger as one system. What is the net force on the system? Explain. **Explanation:** In this scenario, we need to examine the forces acting on the system comprising the cart and the mass hanger. Due to the low friction surface, frictional forces are minimized, allowing us to focus on the primary forces, which include the gravitational force on the mass hanger and any applied forces. #### Exploration 3.2 **Question:** How could you change the net force on the system and keep the total mass of the system constant? Explain. **Explanation:** To alter the net force on the system while maintaining a constant total mass, we can adjust the distribution of the masses between the cart and the mass hanger. For instance, by moving some weight from the cart to the mass hanger, or vice versa, we can change the gravitational force acting on the mass hanger, thereby changing the net force without altering the total mass of the system. #### Exploration 3.3 **Question:** If you were to take data, constantly changing the net force on the system but keeping the total mass the same, what quantity could you plot vs. net force to give a straight line? Explain. Sketch the graph below. **Explanation:** To obtain a straight-line graph, you can plot acceleration (a) versus net force (F). According to Newton’s second law (\( F = ma \)), if the total mass (m) is constant, the relationship between net force and acceleration will be linear. **Graph Sketch:** - **X-axis:** Net Force (F) - **Y-axis:** Acceleration (a) The graph should depict a straight line passing through the origin with a positive slope. **Question:** What physical quantity does the slope of the line represent? Explain in words and equations. **Explanation:** The slope of the line on the graph of acceleration vs. net force represents the reciprocal of the total mass of the system. Mathematically, the slope \( \text{slope} = \frac{1}{m} \), where \( m \) is the total mass. This is derived from rearranging Newton’s second law equation \( F = ma \) to \( a = \frac{
Transcribed Image Text:### Exploration 3: Accelerating the Cart with a Different Net Force and Constant Total Mass #### Exploration 3.1 **Question:** Since the surface is very low friction, it is possible to consider the cart and mass hanger as one system. What is the net force on the system? Explain. **Explanation:** In this scenario, we need to examine the forces acting on the system comprising the cart and the mass hanger. Due to the low friction surface, frictional forces are minimized, allowing us to focus on the primary forces, which include the gravitational force on the mass hanger and any applied forces. #### Exploration 3.2 **Question:** How could you change the net force on the system and keep the total mass of the system constant? Explain. **Explanation:** To alter the net force on the system while maintaining a constant total mass, we can adjust the distribution of the masses between the cart and the mass hanger. For instance, by moving some weight from the cart to the mass hanger, or vice versa, we can change the gravitational force acting on the mass hanger, thereby changing the net force without altering the total mass of the system. #### Exploration 3.3 **Question:** If you were to take data, constantly changing the net force on the system but keeping the total mass the same, what quantity could you plot vs. net force to give a straight line? Explain. Sketch the graph below. **Explanation:** To obtain a straight-line graph, you can plot acceleration (a) versus net force (F). According to Newton’s second law (\( F = ma \)), if the total mass (m) is constant, the relationship between net force and acceleration will be linear. **Graph Sketch:** - **X-axis:** Net Force (F) - **Y-axis:** Acceleration (a) The graph should depict a straight line passing through the origin with a positive slope. **Question:** What physical quantity does the slope of the line represent? Explain in words and equations. **Explanation:** The slope of the line on the graph of acceleration vs. net force represents the reciprocal of the total mass of the system. Mathematically, the slope \( \text{slope} = \frac{1}{m} \), where \( m \) is the total mass. This is derived from rearranging Newton’s second law equation \( F = ma \) to \( a = \frac{
**Lab 6: Force, Mass and Acceleration** **Objectives:** - To study Newton's Second Law, F = ma, with a constant net force - To study Newton’s Second Law with constant mass **Equipments:** - Computer-based laboratory system - Motion detector - Real-time physics mechanics experiment configuration files - Cart - Force probe - Ramp - Masses - White card - Balance **Exploration 1: Force diagrams, net force and acceleration** Consider a cart on a frictionless surface with a light string attached, hanging over a pulley, as in the picture below. Consider the situation after the hanging mass has been released from rest. *(Image description: A diagram shows a cart (labeled as \( m_c \)) on a horizontal surface connected by a light string passing over a pulley to a hanging mass (labeled as \( m_h \)). The string exerts tension on both the cart and the hanging mass.)* **Exploration 1.1.a** Draw two force diagrams – one for the cart and one for the hanging mass in the space below.
Transcribed Image Text:**Lab 6: Force, Mass and Acceleration** **Objectives:** - To study Newton's Second Law, F = ma, with a constant net force - To study Newton’s Second Law with constant mass **Equipments:** - Computer-based laboratory system - Motion detector - Real-time physics mechanics experiment configuration files - Cart - Force probe - Ramp - Masses - White card - Balance **Exploration 1: Force diagrams, net force and acceleration** Consider a cart on a frictionless surface with a light string attached, hanging over a pulley, as in the picture below. Consider the situation after the hanging mass has been released from rest. *(Image description: A diagram shows a cart (labeled as \( m_c \)) on a horizontal surface connected by a light string passing over a pulley to a hanging mass (labeled as \( m_h \)). The string exerts tension on both the cart and the hanging mass.)* **Exploration 1.1.a** Draw two force diagrams – one for the cart and one for the hanging mass in the space below.
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