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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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In the figure, a block of mass m = 19 kg is released from rest on a frictionless incline of angle θ = 30°. Below the block is a spring that can be compressed 1.3 cm by a force of 150 N. The block momentarily stops when it compresses the spring by 5.6 cm. (a) How far does the block move down the incline from its rest position to this stopping point? (b) What is the speed of the block just as it touches the spring?

This diagram depicts a physics scenario involving a block of mass \( m \) on an inclined plane, with an angle of inclination \( \theta \). There is also a spring attached to the base of the incline which is compressed. **Elements of the Diagram:** 1. **Inclined Plane:** - The surface on which the block rests is inclined at an angle \( \theta \) from the horizontal axis. 2. **Block:** - A block with mass \( m \) is situated on the plane. The angle and friction of the inclined plane are significant factors in calculating forces acting on the block. 3. **Spring:** - A spring, attached to a fixed point at the bottom of the incline, is positioned such that it is compressed when the block is in its current position. The potential energy stored in the compressed spring can be calculated using Hooke’s Law, which is given by \( PE_{spring} = \frac{1}{2} k x^2 \) where \( k \) is the spring constant and \( x \) is the compression distance. **Analyzing Forces:** - **Gravitational Force (mg):** - Acts vertically downward. This force can be resolved into two components: - Parallel to the incline: \( mg \sin(\theta) \) - Perpendicular to the incline: \( mg \cos(\theta) \) - **Normal Force:** - Acts perpendicular to the surface of the inclined plane. It counteracts the perpendicular component of the gravitational force. - **Spring Force:** - Acts horizontally along the plane, directed opposite to the compression of the spring. This setup can be used to discuss concepts such as mechanical energy conservation, kinetic and potential energy transformations, and dynamics on an inclined plane. Calculations involving forces and energies will require mechanical equilibrium conditions or applying Newton’s second law of motion.
Transcribed Image Text:This diagram depicts a physics scenario involving a block of mass \( m \) on an inclined plane, with an angle of inclination \( \theta \). There is also a spring attached to the base of the incline which is compressed. **Elements of the Diagram:** 1. **Inclined Plane:** - The surface on which the block rests is inclined at an angle \( \theta \) from the horizontal axis. 2. **Block:** - A block with mass \( m \) is situated on the plane. The angle and friction of the inclined plane are significant factors in calculating forces acting on the block. 3. **Spring:** - A spring, attached to a fixed point at the bottom of the incline, is positioned such that it is compressed when the block is in its current position. The potential energy stored in the compressed spring can be calculated using Hooke’s Law, which is given by \( PE_{spring} = \frac{1}{2} k x^2 \) where \( k \) is the spring constant and \( x \) is the compression distance. **Analyzing Forces:** - **Gravitational Force (mg):** - Acts vertically downward. This force can be resolved into two components: - Parallel to the incline: \( mg \sin(\theta) \) - Perpendicular to the incline: \( mg \cos(\theta) \) - **Normal Force:** - Acts perpendicular to the surface of the inclined plane. It counteracts the perpendicular component of the gravitational force. - **Spring Force:** - Acts horizontally along the plane, directed opposite to the compression of the spring. This setup can be used to discuss concepts such as mechanical energy conservation, kinetic and potential energy transformations, and dynamics on an inclined plane. Calculations involving forces and energies will require mechanical equilibrium conditions or applying Newton’s second law of motion.
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