(32/8)^2=16
Triple the mass will triple the kinetic energy; triple the speed will increase it by a factor of 9 (32), so in total, ball A will have 27 times the kinetic energy of ball B.
Kinetic energy is equal to the mass of the object times the velocity squared (Ek=.5mv2). To obtain the ratio between the two objects, divide the first by the second (Ek1/Ek2). This is equivalent to .5m1v12/.5m2v22. Since the masses are equal, they cancel out and you are left with v12/v22. Next, as stated in the problem, the seceond velocity is twice as much as the first so plug that coefficient into the aforementioned equation. (1v12)/(2v22). Since the values of velocity (v) are equal in this problem, they can cancel out just as the masses did. Now, 12=1 and 22=4; so the ratio is 1/4.
Mechanical energy is the combination of a system's total kinetic and potential energy. Kinetic energy is the energy of movement, is possessed by any objects in motion, and is given by the equation K = (1/2)mv^2. Potential energy has several types, including potential energy due to height (gravitational potential energy) and due to the tension inherent to a spring (elastic potential energy). Ug = mgh, where g is the acceleration due to gravity. Ue = (1/2)kx^2, where k is the spring constant and x is the distance the spring is stretched in meters. Although the universe follows the Law of Conservation of Energy, mechanical energy is not necessarily conserved. This means that mechanical energy can transform into other types of energy and vice versa. For example, when a machine operates, some mechanical energy is lost to heat energy. The ratio of mechanical energy conserved to the energy lost to thermal energy is known as efficiency, and no machines have 100% efficiency (no heat loss). On the other hand, non-mechanical energy such as electrical energy can convert to kinetic energy in situations when the electric potential of a capacitor powers the movement of a particle through the capacitor.
Kinetic energy at velocity "V" is (0.5) x mass x V x V Kinetic energy at velocity "2V" is (0.5) x mass x 2V x 2V Ratio of KE at velocity 2V and KE at velocity V is [(0.5) x mass x 2V x 2V] / [(0.5) x mass x V x V] = 4 So if the velocity double, KE quadruples
Because it is the ratio of two speeds (which will have identical units), the units cancel.
The answer depends on what two (or more) things the ratio is meant to compare. The kinetic energy of several objects? The kinetic energy of an object compared to its total energy? The kinetic energy compared to its engine size?
no
Triple the mass will triple the kinetic energy; triple the speed will increase it by a factor of 9 (32), so in total, ball A will have 27 times the kinetic energy of ball B.
.067
42.8
Kinetic energy is equal to the mass of the object times the velocity squared (Ek=.5mv2). To obtain the ratio between the two objects, divide the first by the second (Ek1/Ek2). This is equivalent to .5m1v12/.5m2v22. Since the masses are equal, they cancel out and you are left with v12/v22. Next, as stated in the problem, the seceond velocity is twice as much as the first so plug that coefficient into the aforementioned equation. (1v12)/(2v22). Since the values of velocity (v) are equal in this problem, they can cancel out just as the masses did. Now, 12=1 and 22=4; so the ratio is 1/4.
Mechanical energy is the combination of a system's total kinetic and potential energy. Kinetic energy is the energy of movement, is possessed by any objects in motion, and is given by the equation K = (1/2)mv^2. Potential energy has several types, including potential energy due to height (gravitational potential energy) and due to the tension inherent to a spring (elastic potential energy). Ug = mgh, where g is the acceleration due to gravity. Ue = (1/2)kx^2, where k is the spring constant and x is the distance the spring is stretched in meters. Although the universe follows the Law of Conservation of Energy, mechanical energy is not necessarily conserved. This means that mechanical energy can transform into other types of energy and vice versa. For example, when a machine operates, some mechanical energy is lost to heat energy. The ratio of mechanical energy conserved to the energy lost to thermal energy is known as efficiency, and no machines have 100% efficiency (no heat loss). On the other hand, non-mechanical energy such as electrical energy can convert to kinetic energy in situations when the electric potential of a capacitor powers the movement of a particle through the capacitor.
30 J
Kinetic Energy = 1/2 m V2At 2 m/s, the bicycle's KE is (1/2 x 10 x 4) = 20 joules.At 3 m/s, its KE is (1/2 x 10 x 9) = 45 joules.The difference in kinetic energy at the higher speed is (45 - 20) = 25 joules.That's the energy (work) that has to come from somewhere in order to achievethe higher speed.Check:The ratio of speeds is 3/2 = 1.5 . Since kinetic energy is proportional to the square of the speed,we need the square of the ratio to check. It's (1.5)2 = 2.25 .The ratio of the kinetic energies that we calculated at the two speeds is (45/20) = 2.25 .That's good enough for us. Check ! and mate
protons and electrons are identical in number in an atom
Density
The efficiency ratio for a machine usually refers to the ratio of the useful energy available from a machine and the energy put into it.