Projectile Motion in Combination with Energy Problem

In summary, the problem involves a toy rifle shooting a spring with a mass of 0.008kg and a spring constant of 350 N/m. The goal is to hit a target 15m away by pointing the rifle 45 degrees above the horizontal. To find the correct spring compression length, we can use the formula for horizontal range in projectile motion and set sin2θ to 1. This will give us the initial velocity needed, from which we can calculate the kinetic energy and potential energy of the spring. By modifying the equation for potential energy, we can determine the spring compression length required to reach the target.
  • #1
Bound
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Homework Statement


A toy rifle shoots a spring of mass 0.008kg and with a spring constant of 350 N/m. You wish to hit a target horizontally a distance of 15m away by pointing the rifle 45o above the horizontal. How far should you extend the spring in order to reach the target?


Homework Equations


E = 1/2(k)(x)2
F = kx
KE = 1/2(m)(v)2
Any relevant kinematics formulae.


The Attempt at a Solution


Normally for questions like this I would equate potential spring energy to the kinetic energy, but here I am missing a velocity as well as the spring compression length so I am a little lost.
 
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  • #2
Bound said:

Homework Statement


A toy rifle shoots a spring of mass 0.008kg and with a spring constant of 350 N/m. You wish to hit a target horizontally a distance of 15m away by pointing the rifle 45o above the horizontal. How far should you extend the spring in order to reach the target?


Homework Equations


E = 1/2(k)(x)2
F = kx
KE = 1/2(m)(v)2
Any relevant kinematics formulae.


The Attempt at a Solution


Normally for questions like this I would equate potential spring energy to the kinetic energy, but here I am missing a velocity as well as the spring compression length so I am a little lost.
Use the formula for horizontal range for projectile motion letting sin2θ = 1 and R = 15 m. to determine the initial velocity v that is needed. From that you can work out the kinetic energy and, therefore, the potential energy of the spring.

AM
 

Related to Projectile Motion in Combination with Energy Problem

1. What is projectile motion and how does it relate to energy problems?

Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity. It is directly related to energy problems because the object's kinetic and potential energy are constantly changing as it moves through the air due to the force of gravity.

2. How does the angle of launch affect the projectile's motion and energy?

The angle of launch is a crucial factor in determining the path and energy of a projectile. A higher angle of launch will result in a longer flight time and a higher peak height, meaning that the projectile will have a greater potential energy at its highest point. However, a lower angle of launch will result in a shorter flight time and a lower peak height, meaning that the projectile will have less potential energy.

3. Can you explain the concept of conservation of energy in relation to projectile motion?

Conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. In projectile motion, the total energy of the object (kinetic + potential) remains constant throughout its motion, even as it is transferred between the two forms. This is why a projectile will have the same amount of energy at the beginning and end of its flight, even though its kinetic and potential energy may have changed.

4. How does air resistance affect the projectile's energy and trajectory?

Air resistance, also known as drag, is a force that opposes the motion of an object through the air. As a projectile moves through the air, it experiences air resistance which decreases its kinetic energy and alters its trajectory. This means that the projectile will not travel as far and will have less energy than it would have in a vacuum. The amount of air resistance depends on the size, shape, and speed of the projectile.

5. How can we use the equations for energy and motion to solve projectile motion problems?

To solve projectile motion problems, we can use the equations for energy and motion to calculate the initial velocity, time of flight, maximum height, and range of the projectile. By setting up and solving equations for the projectile's kinetic and potential energy at different points in its motion, we can determine its energy at any given time. We can then use this information to find its position or other variables at any point in its trajectory.

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