A marble moving at a constant speed of 3 m/s possesses 333 J of kinetic energy. What is the ball mass
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Answer:
Kinetic Energy (From The Sciences, 6th ed., by Trefil and Hazen)
Think about a cannonball flying through the air. When it hits a wooden target, the ball exerts a force on the fibers in the wood, splintering and pushing them apart and creating a hole. Work has to be done to make that hole; fibers have to be moved aside, which means that a force must be exerted over the distance they move. When the cannonball hits the wood, it does work, and so a cannonball in flight clearly has the ability to do work—that is, it has energy—because of its motion. This energy of motion is what we call kinetic energy.
You can find countless examples of kinetic energy in nature. A whale moving through water, a bird flying, and a predator catching its prey all have kinetic energy. So do a speeding car, a flying Frisbee, a falling leaf, and anything else that is moving.
Our intuition tells us that two factors govern the amount of kinetic energy contained in any moving object. First, heavier objects that are moving have more kinetic energy than lighter ones: a bowling ball traveling 10 m/s (a very fast sprint) carries a lot more kinetic energy than a golf ball traveling at the same speed. In fact, kinetic energy is directly proportional to mass: if you double the mass, then you double the kinetic energy.
Second, the faster something is moving, the greater the force it is capable of exerting and the greater energy it possesses. A high-speed collision causes much more damage than a fender bender in a parking lot. It turns out that an object’s kinetic energy increases as the square of its speed. A car moving 40 mph has four times as much kinetic energy as one moving 20 mph, while at 60 mph a car carries nine times as much kinetic energy as at 20 mph. Thus a modest increase in speed can cause a large increase in kinetic energy.
These ideas are combined in the equation for kinetic energy.
In words: Kinetic energy equals the mass of the moving object times the square of that object’s speed (v2).
In equation form: kinetic energy (joules) = 1/2 x mass (kg) x velocity2 (m/s)
In symbols: KE = 1/2 x m x v2
Examples: Bowling Balls and Baseballs What is the kinetic energy of a 4-kg (about 8-lb) bowling ball rolling down a bowling lane at 10 m/s (about 22 mph)?