# Potential Energy: Energy that is stored in an object as a result of its position or condition. Gravitational Potential Energy: depends on the mass in addition to the height of the object. Solution to Example 1

## Potential Energy: Energy that is stored in an object as a result of its position or condition. Gravitational Potential Energy: depends on the mass in addition to the height of the object. Solution to Example 1

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Bellwork SolutionThe only as long as ce doing work is gravity. Since it is an internal or conservative as long as ce, the total mechanical energy is conserved. Thus, the 100 J of original mechanical energy is present at each position. So the KE as long as A is 50 J.The PE at the same stairstep is 50 J (C) in addition to thus the KE is also 50 J (D).The PE at zero height is 0 J (F in addition to I). And so the kinetic energy at the bottom of the hill is 100 J (G in addition to J).Using the equation KE = 0.5mv2, the velocity can be determined to be 7.07 m/s as long as B in addition to E in addition to 10 m/s as long as H in addition to K. Work Done by a Variable ForcePotential Energy, Spring Force in addition to Hookes LawObjectives: Define in addition to underst in addition to potential energyCalculate the work done by a spring as long as ce.Study the Work-Energy Theorem in addition to apply it in solving problems.Potential Energy: Energy that is stored in an object as a result of its position or condition.Chemical  energy stored in bonds between atomsGravitational  energy stored as a result of an objects vertical position, or heightElastic  energy stored in material as a result of stretching or compression

Gravitational Potential Energy: depends on the mass in addition to the height of the object.Potential energy = mass x gravity x heightzero height position must first be assigned.Typically, the ground is considered to be a position of zero height. Example 1: A cart is loaded with a brick in addition to pulled at constant speed along an inclined plane to the height of the top of a chair. If the mass of the loaded cart is 3.0 kg in addition to the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-topSolution to Example 1Given:m = 3 kgg = 9.8 m/s2h = 0.45 mPE = mgh PE = (3 kg ) (9.8 m/s/s) (0.45 m)PE = 13.2 J

Example 2: If a as long as ce of 14.7 N is used to drag the loaded cart (from previous question) along the incline as long as a distance of 0.90 meters, then how much work is done on the loaded cartSolution to Example 2Given: F= 14.7 N d= 0.9 m q = 0oW = F d cos Theta W = 14.7 N 0.9 m cos (0 degrees)W = 13.2 JElastic Potential Energy: Spring ForcesSprings are a device which can store elastic potential energy due to either compression or stretching. A as long as ce is required to compress a spring; the more compression there is, the more as long as ce which is required to compress it further. For certain springs, the amount of as long as ce is directly proportional to the amount of stretch or compression (x); the constant of proportionality is known as the spring constant (k).

Calculating the Spring ForceHooke’s LawFspring = k x where k is the spring constant in addition to x is the amount of stretch or compression. If a spring is not stretched or compressed, then there is no elastic potential energy stored in it. The spring is said to be at its equilibrium position. The equilibrium position is the position that the spring naturally assumes when there is no as long as ce applied to it.Calculating Elastic Potential Energy The amount of elastic potential energy is related to the amount of stretch (or compression) in addition to the spring constant. The equation isThe work done by an external as long as ce in stretching or compressing a spring (to overcome the spring as long as ce) is calculated by: Where k is the spring constant in addition to x is the stretch or compression distance from the equilibrium position

Example 3: A spring of spring constant 20 N/m is to be compressed by 0.10 m. A) what is the maximum as long as ce requiredB) What is the work requiredSolution to Example 3Given: k = 20 N/mx = -0.10 mFor a compression, F = -kxW = ½ kx2F = -(20 N/m)(-0.10 m) = 2.0 NW = ½ (20 N/m)(-0.10 m)2 = 0.10 JRound the Clock Spring ProblemsDraw a circle, or clock on your paper in addition to divide it into 4ths.Set 4 appointments with your classmates; one at 12 oclock, one at 3 oclock, one at 6 oclock, in addition to one at 9 oclock. Solve the following problems at your appointment.

Round the Clock Spring Problems 3 oclock: When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the as long as ce constant of the spring.6 oclock: If a spring has a spring constant of 400 N/m, how much work is required to compress the spring 25.0 cm from its undisturbed position9 oclock: A compressed spring that obeys Hooke’s law has a potential energy of 18 J. If the spring constant of the spring is 400 N/m, find the distance by which the spring is compressed. 12 oclock: To compress spring 1 by 0.20 m takes 150 J of work. Stretching spring 2 by 0.30 m requires 210 J of work. Which spring is stiffer Kinetic Energy: energy of motionAn object which has motion – whether it be vertical or horizontal motion – has kinetic energy. Vibrational : the energy due to vibrational motion Rotational: the energy due to rotational motionTranslational: the energy due to motion from one location to anotherThe amount of translational kinetic energy an object has depends upon two variables: the mass (m) of the object in addition to the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.

3 oclock: Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s. 6 oclock: If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy 9 oclock: Missy Diwater, the as long as mer plat as long as m diver as long as the Ringling Brother’s Circus, had a kinetic energy of 12 000 J just prior to hitting the bucket of water. If Missy’s mass is 40 kg, then what is her speed 12 oclock: A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic energy if it is moving at 30 mi/hr. The Work-Energy TheoremThe net work done on an object is equal to its change in kinetic energy.W = K  K0 = DKWork is a measure of energy transfer.Energy is the capacity to do work.The net as long as ce acting on an object causes the object to accelerate, changing its velocity:Combining Kinematic Equations in addition to Newtons Second Law

Example 4: The opposing kinetic friction as long as ce between a 60.0 kg object in addition to a horizontal surface is 50.0 N. If the initial speed of the object is 25.0 m/s, what distance will it slide be as long as e coming to a stop FnormFfric FgravSolution to Example 4Given:m = 60.0 kg Ffric = 50.0 Nv0 = 25.0 m/s v = 0 m/s W = K-K0W = (Fcosq)d = (Ffriccos180)dW = K-K0= ½ mv2  ½ mv02(50.0 N)(cos180)(d ) = ½(60.0kg)(0m/s)2-1/2(60.0 kg)(25.0 m/s)2d = 3.75 x 102 mLaw of Conservation of Energy: First Law of ThermodynamicsIf the working as long as ces (the as long as ces doing nonzero work) in a system are conservative, the total mechanical energy of the system is conserved.Conservative Forces: independent of the path but dependent on only the initial in addition to final locations.Nonconservative Forces: the work done by or against it depends on the path (friction, as long as example)E = KE + PEKE0+PE0 = KE + PE½ mv2 + mgh = ½ mv02 + mgh0

Independent PracticeConservation of Energy  Work with your Best Partner to solve the problems related to total Mechanical Energy.E = KE + PEHomework: Work Done by a Variable Force

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