A 2.1 kg breadbox on a frictionless incline of angle θ = 42 ˚ is connected, by a cord that runs over a pulley, to a light spring of spring constant k = 120 N/m, as shown in the figure. The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10.8 cm down the incline? (b) How far down the incline from its point of release does the box slide before momentarily stopping, and what are the (c) magnitude and (d) direction of the box's acceleration at the instant the box momentarily stops? **Pulley System on an Inclined Plane**The diagram illustrates a pulley system set up on an inclined plane, demonstrating the principles of mechanics and motion. Here’s a detailed explanation of the different components:1. **Inclined Plane**: This is represented as a sloped surface inclined at an angle θ (theta) to the horizontal. Inclined planes are commonly used to facilitate the movement of heavy objects upward or downward with less effort. The angle θ affects the force required to move an object and can be calculated using trigonometric functions.2. **Pulley**: Positioned at the top of the inclined plane, the pulley in the system helps in redirecting the tension force in the rope or cable. Pulleys reduce the amount of effort needed to lift or move an object by changing the direction of the force applied.3. **Spring**: Connected to the upper end of the inclined plane and extending horizontal towards the pulley, the spring represents elastic force. This type of setup is used to study the force exerted by the spring due to its extension or compression based on Hooke’s Law \(F = -kx\), where \(k\) is the spring constant and \(x\) is the displacement from its equilibrium position.4. **Rope/Cable**: The rope or cable runs over the pulley and is attached to the object placed on the inclined plane. This component is instrumental in transmitting the force applied to move the object either up or down the incline.5. **Object**: This is the rectangular block placed on the inclined plane. The object can represent any mass that needs to be moved or held stationary on the plane. The forces acting on this object include gravitational force, normal force, frictional force (if applicable), and the tension in the rope.Through this diagram, students can understand how forces interact in a system involving multiple elements. By analyzing this setup, principles such as equilibrium, Newton’s laws of motion, friction, inclined plane mechanics, and Hooke’s Law can be explored and understood in practical scenarios.

Name: A 2.1 kg breadbox on a frictionless incline of angle θ = 42 ˚ is conne
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: A 2.1 kg breadbox on a frictionless incline of angle θ = 42 ˚ is connected, by a cord that runs over a pulley, to a light spring of spring constant k = 120 N/m, as shown in the figure. The box is released from rest when the spring is unstretched. Ass