Physics 2015 – Mechanical Energy Conservation
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Physics 2015 – Mechanical Energy Conservation
Study energy conservation by looking at the relationship between three different types of energy:
• Gravitational Potential Energy (GPE)
• Elastic Potential Energy (EPE)
• Kinetic Energy (KE)
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Physics 2015 – Mechanical Energy Conservation
Energy is conserved if we can add up all of the different types of energy acting in a closed system and see that the total sum is constant.
• A “closed system” is one where no energy is added to or taken away from the system (in our case, a system with negligible friction)
• The types of energy will change depending on the setup. Ours were listed on the previous slide.
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Physics 2015 – Mechanical Energy Conservation
Different Energy Types
• Gravitational Potential Energy (GPE) – the energy due to gravity
𝑮𝑷𝑬 = 𝒎𝒈𝒉
• Elastic Potential Energy (EPE) – the energy in a spring, where k = spring constant
𝟏
𝑬𝑷𝑬 = 𝒌𝒙
𝟐
𝟐
• Kinetic Energy (KE) – the energy due to motion
𝟏
𝑲𝑬 = 𝒎𝒗 𝟐
𝟐
• Heat Energy (such as friction, sound, etc.)
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Physics 2015 – Mechanical Energy Conservation photogate
Note as the cart is released, the quantity
GPE + EPE + KE should stay the same. We will be able to measure all three at any two different points of the cart’s travel.
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Physics 2015 – Mechanical Energy Conservation
Activity 1 – Find the Spring Constant (k)
• We will find this constant using Hooke’s Law:
𝑭 = −𝒌𝒙
• In the setup on the last page, attach a few masses to the string hanging off the table, and measure how the spring stretches from its rest length.
• You can then plot your data in Excel, and use a linear regression, where the slope = -k.
mg
Department of Physics & Astronomy slope = -k
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Physics 2015 – Mechanical Energy Conservation
Activity 2 – Conservation of Energy
• First, decide where you want to make your GPE
= 0. Note that a good choice will make your calculations much easier!
• Measure ALL of the masses, including the mass of the cart, since this will be needed for your calculations!
• Then, use your equations to calculate GPE, EPE, and KE for a cart without mass on the top, and for a cart with mass.
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Physics 2015 – Mechanical Energy Conservation
• Remember that percent energy change is:
𝑬 𝒇𝒊𝒏𝒂𝒍
% 𝑬𝒏𝒆𝒓𝒈𝒚 𝑪𝒉𝒂𝒏𝒈𝒆 =
− 𝑬 𝒊𝒏𝒊𝒕𝒊𝒂𝒍 𝒎 𝒉𝒂𝒏𝒈𝒊𝒏𝒈 𝒈(∆𝒙)
• Note in this setup that 𝒎 𝒉𝒂𝒏𝒈𝒊𝒏𝒈
= mass off the edge of the table (excluding cart), and Δx is the spring length change (which is also the change in height of the mass!)
• If you do find an energy change is not zero, ask if your system was “totally closed.” Was some energy not accounted for?
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