Conservation of Mechanical Energy

In summary, the conversation discusses the problem of finding the kinetic energy and work done on a 1.0 kg projectile fired from the Earth's surface at an angle of 45° with an initial velocity of 30 m/s. The equations for total mechanical energy and work are mentioned, and the attempt at a solution includes identifying known values and using equations to solve for unknown values. The conversation ends with a request for further guidance on projectile motion.
  • #1
domtar
6
0

Homework Statement



A 1.0 kg projectile is fired from a point on the Earth's surface at an angle θ = 45° with the horizontal and with an initial velocity v = 30 m/s. Neglect any effects due to air resistance and find:

a) What is the kinetic energy of the projectile when it reaches the highest point on its trajectory?
b) How much work was done in firing the projectile?

Homework Equations



total mechanical energy = KE + PE

KE_i + PE_i + W = KE_f + PE_f

The Attempt at a Solution



I'm not sure how to start this problem, or how to tackle it. I'm assuming I have to use the second equation? I let KE = 1/2 mv^2, m=1.0kg, v=30m/s. Then PE=mgh, m=1.0kg, g=9.81m/s/s, h=?. Then W=Fdcosθ, F=?, d=? cosθ=cos45°. Then I'm sort of stuck... There's a lot of values missing and I'm not sure how to solve or where to start.

Any help would be appreciated, thank you.
 
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  • #2
Hi domtar,

The keyword is "projectile". What do you know about projectile motion?

ehild
 

FAQ: Conservation of Mechanical Energy

What is the law of conservation of mechanical energy?

The law of conservation of mechanical energy states that in a closed system, the total amount of mechanical energy (the sum of kinetic and potential energy) remains constant over time. This means that energy cannot be created or destroyed, but can only be transferred from one form to another.

How does the law of conservation of mechanical energy relate to the concept of work?

The law of conservation of mechanical energy is closely related to the concept of work because work is defined as a change in energy. In other words, when work is done on an object, its energy (either kinetic or potential) changes. The total amount of energy, however, remains constant due to the law of conservation of mechanical energy.

Can the law of conservation of mechanical energy be violated?

No, the law of conservation of mechanical energy is a fundamental principle in physics that has been observed and tested in countless experiments. It has been shown to hold true in all known physical systems and cannot be violated.

What are some real-life examples of the law of conservation of mechanical energy in action?

Some common examples of the law of conservation of mechanical energy include a pendulum swinging back and forth, a roller coaster moving along its track, and a bouncing ball. In all of these situations, the total mechanical energy of the system remains constant despite changes in kinetic and potential energy.

How is the law of conservation of mechanical energy applied in the field of engineering?

The law of conservation of mechanical energy is an important principle in engineering, especially in the design of machines and structures. Engineers must carefully consider how energy is transferred and conserved in their designs to ensure safe and efficient operation. This law is also used in calculations and simulations to predict the behavior of various mechanical systems.

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