A spring-loaded dart gun is used to shoot a dart straight up into the air. When fully compressed, the dart reaches a maximum height of \( h_1 \) above its release point. The same dart is shot up a second time from the same gun, but this time the spring is compressed at \( 1/2.14 \) as compared to the first shot.How high, \( h_2 \), does the dart go the second time in terms of the maximum height \( h_1 \)? Fill in the missing factor below. (Neglect friction and assume the spring is ideal.)[Hint: Use the first situation to find an expression for the spring constant. Use that expression to solve for the height in the second situation.]\[ h_2 = \, \_\_\_\_\_ \, h_1 \]

A spring-loaded dart gun is used to shoot a dart straight up into the air. When fully compressed, the dart reaches a maximum height of h₁ above its release point. The same dart is shot up a second time from the same gun, but this time the spring is compressed at 1/2.14 as compared to the first shot. How high, h₂, does the dart go the second time in terms of the maximum height h₁? Fill in the missing factor below. (Neglect friction and assume the spring is ideal.) [Hint: Use the first situation to find an expression for the spring constant. Use that expression to solve for the height in the second situation.] h₁ h₂

A spring-loaded dart gun is used to shoot a dart straight up into the air. When fully compressed, the dart reaches a maximum height of h₁ above its release point. The same dart is shot up a second time from the same gun, but this time the spring is compressed at 1/2.14 as compared to the first shot. How high, h₂, does the dart go the second time in terms of the maximum height h₁? Fill in the missing factor below. (Neglect friction and assume the spring is ideal.) [Hint: Use the first situation to find an expression for the spring constant. Use that expression to solve for the height in the second situation.] h₁ h₂

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

A spring-loaded dart gun is used to shoot a dart straight up into the air. When fully compressed, the dart reaches a maximum height of \( h_1 \) above its release point. The same dart is shot up a second time from the same gun, but this time the spring is compressed at \( 1/2.14 \) as compared to the first shot.

How high, \( h_2 \), does the dart go the second time in terms of the maximum height \( h_1 \)? Fill in the missing factor below. (Neglect friction and assume the spring is ideal.)

[Hint: Use the first situation to find an expression for the spring constant. Use that expression to solve for the height in the second situation.]

\[ h_2 = \, \_\_\_\_\_ \, h_1 \]

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