**Problem Description:**An archer pulls her bowstring back 0.408 meters by exerting a force that increases uniformly from zero to 215 Newtons.**Questions:**(a) What is the equivalent spring constant of the bow?- [_____] N/m(b) How much work does the archer do on the string in drawing the bow?- [_____] J**Explanation of Concepts:**- **Spring Constant (k):** This is a measure of the stiffness of a spring, defined as the force required to displace the spring by one unit of length. It can be calculated using Hooke's Law, which states that the force, F, exerted by a spring is proportional to its extension, x: \( F = kx \).- **Work Done:** This refers to the energy transferred when a force is applied over a distance. For a spring-like system, the work done can be calculated using the formula: \( \text{Work} = \frac{1}{2} k x^2 \). Alternatively, if the force varies uniformly, the work done can be calculated as the area under the force-extension graph, which is a triangle in this case. **Graph/Diagram:** There is no graph or diagram provided with this question. The scenario describes a linear increase in force from 0 to 215 N over the displacement of 0.408 meters. The graphical representation would be a right triangle on a force versus displacement graph, with the base (displacement) being 0.408 m and the height (force) being 215 N. The area of this triangle would be used to calculate the work done.

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An archer pulls her bowstring back 0.408 m by exerting a force that increases uniformly from zero to 215 N. (a) What is the equivalent spring constant of the bow? N/m (b) How much work does the archer do on the string in drawing the bow?

An archer pulls her bowstring back 0.408 m by exerting a force that increases uniformly from zero to 215 N. (a) What is the equivalent spring constant of the bow? N/m (b) How much work does the archer do on the string in drawing the bow?

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 Description:**

An archer pulls her bowstring back 0.408 meters by exerting a force that increases uniformly from zero to 215 Newtons.

**Questions:**

(a) What is the equivalent spring constant of the bow?
- [_____] N/m

(b) How much work does the archer do on the string in drawing the bow?
- [_____] J

**Explanation of Concepts:**

- **Spring Constant (k):** This is a measure of the stiffness of a spring, defined as the force required to displace the spring by one unit of length. It can be calculated using Hooke's Law, which states that the force, F, exerted by a spring is proportional to its extension, x: \( F = kx \).

- **Work Done:** This refers to the energy transferred when a force is applied over a distance. For a spring-like system, the work done can be calculated using the formula: \( \text{Work} = \frac{1}{2} k x^2 \). Alternatively, if the force varies uniformly, the work done can be calculated as the area under the force-extension graph, which is a triangle in this case.

**Graph/Diagram:**

There is no graph or diagram provided with this question. The scenario describes a linear increase in force from 0 to 215 N over the displacement of 0.408 meters. The graphical representation would be a right triangle on a force versus displacement graph, with the base (displacement) being 0.408 m and the height (force) being 215 N. The area of this triangle would be used to calculate the work done.

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