if the kinetic energy of an arrow is doubled, by what factor has its speed inreased ?
if its speed is doubled, by what factor does its kinetic energy increase?
2006-11-02 04:57:26 · 6 answers · asked by nice_ girl 1 in Science & Mathematics ➔ Physics
Kinetic energy can be expressed as
KE = 0.5*m*v^2
Doubling the kinetic energy requires increasing the speed by the square root of 2. Where doubling the speed increases the energy by a factor of 4.
2006-11-02 05:00:17 · answer #1 · answered by stever 3 · 2⤊ 0⤋
ke = 1/2 mv^2; KE = 1/2 mV^2; where ke is the kinetic energy at the initial velocity (v) and KE is the kinetic energy at the doubled velocity (V = 2v).
So we have KE/ke = (1/2 m V^2)/(1/2 m v^2) = V^2/v^2 = (2v)^2/v^2 = 4; in which case KE/ke = 4 or KE = 4 ke. The kinetic energy with the doubled velocity is four times the kinetic energy of the initial velocity.
The other answers are correct up to this point, but none showed the ratio KE/ke which explicitly shows why KE = 4 ke when doubling velocity. In general KE = (V/v)^2 ke so KE varies as the square of the velocity ratios.
[This is a good thing to remember because it is very practical knowledge. It points out that if you drive at 60 mph rather than 30 mph, for example, you quadruple (60/30)^2 the kinetic energy of your car. All other things equal, it would take you four times the distance to stop it.]
2006-11-02 05:19:48 · answer #2 · answered by oldprof 7 · 1⤊ 0⤋
This question does not explain exactly HOW the kinetic energy has been increased. Other answers here are correct if the arrow is the same in both cases, however, if the kinetic energy is doubled by doubling the mass of the arrow, the speed does not change.
Thus the answer (as shown by others here) must be given with the stipulation that the mass is the same.
2006-11-02 05:12:01 · answer #3 · answered by warmspirited 3 · 1⤊ 1⤋
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2016-10-21 03:49:43 · answer #4 · answered by ? 4 · 0⤊ 0⤋
KE = 1/2mv^2
If the KE is doubled, the velocity is increased by a factor of sqrt.2
If the speed is doubled, the KE increases by a factor of 4.
2006-11-02 05:06:37 · answer #5 · answered by quark_sa 2 · 1⤊ 0⤋
ke=(1/2)mv^2
if ke is doubled, speed must have increased by √2 or a factor of 1.414.
2006-11-02 04:59:50 · answer #6 · answered by yupchagee 7 · 1⤊ 0⤋