A block of mass 4.2 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 405 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 39°. A: The block, starting from rest, slides down the ramp a distance 45 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest? B: After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring? C: What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?
A block of mass 4.2 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 405 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 39°. A: The block, starting from rest, slides down the ramp a distance 45 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest? B: After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring? C: What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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A block of mass 4.2 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 405 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 39°.
A: The block, starting from rest, slides down the ramp a distance 45 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest?
B: After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring?
C: What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?
Transcribed Image Text:The image depicts a block of mass \( M \) positioned on an inclined plane. The incline is at an angle \( \theta \) with the horizontal. The block is attached to a spring on the left side. The spring is shown compressed, indicating potential energy stored within it. The distance from the initial position of the block to the point where it is fully extended/compressed is labeled as \( d \).
Key elements in the diagram:
- **Inclined Plane:** A sloped surface which facilitates the study of motion and forces acting on the block.
- **Block \( M \):** Represents an object with a specified mass, illustrating the effects of gravity, inclined plane forces, and spring force.
- **Spring:** Attaches to the block, depicting potential energy through compression or stretching. It suggests a restoring force that will act on the block when released.
- **Angle \( \theta \):** The inclination of the plane, a crucial parameter in calculating the components of gravitational force acting along and perpendicular to the plane.
- **Distance \( d \):** The horizontal measurement indicating how far the spring is compressed or extended from its equilibrium position.
This setup is typically used to explore concepts such as gravitational force components, normal force, spring force, energy conservation, and harmonic motion on inclined planes.
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