**Problem 4:**A 3 kg block sits on a ramp, against a spring. The spring is compressed by 4 cm when the block is pulled back. The block then moves 1.4 m up the ramp, reaching a height of 0.5 m higher than its initial position before stopping. The kinetic friction force acting on the block from the ramp is \( K = 7 \, \text{N} \).**Objective:**Find the spring constant \( k \).**Diagram:**The image shows a right triangle representing the ramp. The ramp is 1.4 meters long, with a vertical height of 0.5 meters. A block is shown sitting on the ramp.**Equation Table:**The table is set up to show the relationship:\[E_f = E_i + W\]where:- \( E_f \) is the final energy- \( E_i \) is the initial energy- \( W \) is the work done by frictionThe table has three columns corresponding to these variables, but no values are filled in.

Answered: Image /qna-images/answer/d4349293-c535-42a7-8c23-552fe0d0cef1.jpg

4. A 3kg block sits on a ramp, against a spring. I pull back on the block, compressing the string by 4cm, and the block moves 1.4m up the ramp, so that it is 0.5m higher than it was before, before it stops. If the force of kinetic friction on the block from the ramp is K = 7N, find the spring constant k. Ef = Ei 0.5m + 1.4m W

4. A 3kg block sits on a ramp, against a spring. I pull back on the block, compressing the string by 4cm, and the block moves 1.4m up the ramp, so that it is 0.5m higher than it was before, before it stops. If the force of kinetic friction on the block from the ramp is K = 7N, find the spring constant k. Ef = Ei 0.5m + 1.4m W

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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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

**Problem 4:**

A 3 kg block sits on a ramp, against a spring. The spring is compressed by 4 cm when the block is pulled back. The block then moves 1.4 m up the ramp, reaching a height of 0.5 m higher than its initial position before stopping. The kinetic friction force acting on the block from the ramp is \( K = 7 \, \text{N} \).

**Objective:**

Find the spring constant \( k \).

**Diagram:**

The image shows a right triangle representing the ramp. The ramp is 1.4 meters long, with a vertical height of 0.5 meters. A block is shown sitting on the ramp.

**Equation Table:**

The table is set up to show the relationship:

\[
E_f = E_i + W
\]

where:
- \( E_f \) is the final energy
- \( E_i \) is the initial energy
- \( W \) is the work done by friction

The table has three columns corresponding to these variables, but no values are filled in.

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