### Air Track and Hanging Block SystemThe figure shows an air track setup, where a cart (mass $ m_1 = 0.520 \, \text{kg} $) is connected by a cord to a hanging block (mass $ m_2 = 0.180 \, \text{kg} $). The cart starts at coordinates $(-0.500 \, \text{m}, 0 \, \text{m})$, and the block's center is initially at $(0, -0.100 \, \text{m})$. The cord and pulley are considered massless, and friction is negligible.#### Questions:**(a)** Find the acceleration of the center of mass in unit-vector notation:\[ \vec{a}_{\text{com}} = \boxed{\phantom{---}} \, \text{m/s}^2 \]**(b)** Determine the velocity of the center of mass as a function of time $ t $:\[ \vec{V}_{\text{com}} = \boxed{\phantom{---}} \, \text{m/s} \]**(c)** Sketch the path of the system’s center of mass. (Submit a file with max size 1 MB.)**(d)** Describe the path:- ☐ Bulges upward to the right - ☐ Bulges downward to the left - ☐ Straight If the path is straight, find the angle between it and the x-axis (counterclockwise from +x-axis).\[ \boxed{\phantom{-}}^\circ \]#### Diagram Description:- **Diagram**: Shows a side view of a cart on an air track attached to a block via a pulley. The x- and y-axes are marked, with positive x being to the right and positive y being upward. The cart is labeled $ m_1 $ and the block $ m_2 $.

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Description: ### Air Track and Hanging Block SystemThe figure shows an air track setup, where a cart (mass $ m_1 = 0.520 \, \text{kg} $) is connected by a cord to a hanging block (mass $ m_2 = 0.180 \, \text{kg} $). The cart starts at coordinates \((-0.500 \

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The figure below shows an arrangement with an air track, in which a cart is connected by a cord to a hanging block. The cart has mass m, = 0.520 kg and its center is initially at xy coordinates (-0.500 m, 0 m). The block has mass m2 = 0.180 kg and its center is initially at xy coordinates (0, -0.100 m). The mass of the cord and pulley are negligible. The cart is released from rest, and both cart and block move until the cart hits the pulley. The friction between the cart and the air track and between the pulley and its axle is negligible. (a) In unit-vector notation what is the acceleration of the center of mass of the cart-block system? (Express your answer in vector form.) dcom = m/s? (b) What is the velocity of the center of mass as a function of time t? (Assume t is in seconds.) (Express your answer in vector form.) com = m/s

The figure below shows an arrangement with an air track, in which a cart is connected by a cord to a hanging block. The cart has mass m, = 0.520 kg and its center is initially at xy coordinates (-0.500 m, 0 m). The block has mass m2 = 0.180 kg and its center is initially at xy coordinates (0, -0.100 m). The mass of the cord and pulley are negligible. The cart is released from rest, and both cart and block move until the cart hits the pulley. The friction between the cart and the air track and between the pulley and its axle is negligible. (a) In unit-vector notation what is the acceleration of the center of mass of the cart-block system? (Express your answer in vector form.) dcom = m/s? (b) What is the velocity of the center of mass as a function of time t? (Assume t is in seconds.) (Express your answer in vector form.) com = m/s

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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### Air Track and Hanging Block System

The figure shows an air track setup, where a cart (mass $ m_1 = 0.520 \, \text{kg} $) is connected by a cord to a hanging block (mass $ m_2 = 0.180 \, \text{kg} $). The cart starts at coordinates $(-0.500 \, \text{m}, 0 \, \text{m})$, and the block's center is initially at $(0, -0.100 \, \text{m})$. The cord and pulley are considered massless, and friction is negligible.

#### Questions:

**(a)** Find the acceleration of the center of mass in unit-vector notation:
\[ \vec{a}_{\text{com}} = \boxed{\phantom{---}} \, \text{m/s}^2 \]

**(b)** Determine the velocity of the center of mass as a function of time $ t $:
\[ \vec{V}_{\text{com}} = \boxed{\phantom{---}} \, \text{m/s} \]

**(c)** Sketch the path of the system’s center of mass. (Submit a file with max size 1 MB.)

**(d)** Describe the path:
- ☐ Bulges upward to the right
- ☐ Bulges downward to the left
- ☐ Straight

If the path is straight, find the angle between it and the x-axis (counterclockwise from +x-axis).
\[ \boxed{\phantom{-}}^\circ \]

#### Diagram Description:
- **Diagram**: Shows a side view of a cart on an air track attached to a block via a pulley. The x- and y-axes are marked, with positive x being to the right and positive y being upward. The cart is labeled $ m_1 $ and the block $ m_2 $.

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