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Answer:
Potential energy is the energy stored in an object because of its position or configuration, ready to do work when released. For example, when you lift a book, you do work against gravity and the book gains gravitational potential energy which depends on its mass, height, and gravity. When you stretch a rubber band or slinky, you store elastic potential energy in the material due to deformation; release converts this to kinetic energy. In a wound toy car, energy is stored as elastic potential energy in the spring. All these examples show energy transfer from your muscles (work) to stored energy, which can later convert into motion or heat. Remember: potential energy is not visible movement, but stored capacity to do work.
Answer:
The formula for gravitational potential energy is GPE = mgh, where m is mass, g is acceleration due to gravity, and h is height above a
Answer:
Elastic potential energy is stored when an elastic object is stretched or compressed, changing its shape. In the rubber band experiment, pulling the band does work on it; its molecules are displaced, storing energy as elastic potential energy. When released, this stored energy converts quickly into kinetic energy, making the band snap back. In a slinky, both stretching and compressing store elastic energy; release converts it to motion. Factors affecting elastic potential energy include the amount of deformation (stretch/compression distance), the stiffness or elastic constant of the material (a stiffer material stores more energy per unit deformation), and temperature (extreme temperatures can alter elasticity). More deformation and higher stiffness mean more stored elastic energy.
Answer:
Winding the spring stores elastic potential energy: more windings mean more deformation of the spring and therefore greater stored energy. When released, this energy converts into kinetic energy propelling the car. Thus, generally, more windings → greater stored energy → car travels farther. However, not all stored energy becomes motion; some energy is lost as heat due to internal friction in the spring and friction between wheels and surface, and as air resistance. These losses reduce the kinetic energy available for motion, causing the car to stop even though some potential energy remains dissipated as heat. Good lubrication and smoother surfaces reduce friction and increase distance traveled.
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Experiment: Use a ball, meter scale, and stopwatch or marked floor. Lift the ball to different heights (e.g., 0.5 m, 1.0 m, 1.5 m) and release, measuring the impact sound, or better, measure time to hit ground or use a motion sensor to record speed on impact. Observations: As height increases, the ball gains more gravitational potential energy, converting to greater kinetic energy on descent, so speed on impact will be larger. If measuring rebound height, a higher drop usually produces a higher rebound (if elastic). Precautions: Ensure safe area, keep hands away while releasing, use same ball to avoid shape changes, repeat trials for average, and use soft landing to avoid damage. This shows GPE ∝ height.
Answer:
Elastic potential energy in a spring is given by U = (1/2) k x^2, where k is the spring constant and x is displacement. With x = 0.10 m, initial energy U1 = 0.5 × k × (0.10)^2 = 0.005 k. If k is doubled (k' = 2k) and displacement is same, U2 = 0.5 × (2k) × (0.10)^2 = 0.01 k = 2 × U1. Thus the stored energy doubles. Qualitatively, a stiffer spring (higher k) resists deformation more, so pulling the same distance requires more work and stores more energy. So doubling stiffness while keeping displacement constant directly doubles the stored elastic potential energy.
Answer:
For equal mass m, GPE = mgh. Object A at height h has energy U1 = mgh. Object B at 2h has U2 = mg(2h) = 2mgh, i.e., twice the potential energy. On release, in absence of air resistance, all GPE converts into kinetic energy (KE) just before impact: KE = 1/2 m v^2 = mgh (or 2mgh). Solving for speed v: v = sqrt(2gh) for A and v = sqrt(4gh) = sqrt(2) × sqrt(2gh) = sqrt(2) × v_A for B. So the object dropped from double height strikes with √2 times greater speed, and has twice the kinetic energy, showing direct proportionality of GPE with height and nonlinear relation to speed.
Answer:
In the bow-and-arrow experiment, when you draw the bowstring, you do work and store elastic potential energy in the bent bow limbs. On release, elastic potential energy converts into kinetic energy of the arrow, making it fly. According to the conservation of energy, the initial energy supplied equals the sum of energies after release: mainly the arrow’s kinetic energy plus energy stored briefly as vibrational energy in the bow. Energy losses occur as heat due to internal friction in the bow material, sound energy (the twang), and air resistance acting on the arrow. Total energy remains conserved, but useful kinetic energy is reduced by these dissipative losses.
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Method to find k: Use Hooke’s law F = kx. Hang known masses from the spring vertically and measure displacement x for each mass. Force F = mg for each mass. Plot F (y-axis) vs x (x-axis). The slope of the straight line gives k. Alternatively, use a force sensor. Once k is known, compute elastic potential energy U = (1/2) k x^2 for various compressions x used in the toy. Analysis: Ensure measurements are within elastic limit (spring returns to original length). Repeat measurements and average to reduce errors. Account for measurement precision and remove mass of spring if significant. This gives quantitative relation between compression and stored energy.
Answer:
Hydroelectric dams store water at height, giving it gravitational potential energy U = mgh. When water is released, it flows down through turbines; GPE converts into kinetic energy and then into mechanical energy of turbines and finally electrical energy via generators. Power output depends on mass flow rate (ṁ), height (h) called head, and gravitational acceleration g: Power ≈ ṁ g h × efficiency. Factors affecting output: larger head and greater flow increase power. Energy losses include friction in pipes, turbine and generator inefficiencies, air resistance, and leakages. Environmental factors (siltation reducing head) and seasonal flow variations also affect available potential energy and power generation. Efficient design minimizes losses maximizing usable energy.