If a rod is moving at a velocity equal to 1/2 the speed of light parallel to its length, what will a stationary observer observe about its length?
The length of the rod will become exactly half of its original value.
The length of the rod remains the same.
The length of the rod will decrease.
The length of the rod will increase.
I would think D
L=L₀•sqrt{1-(v/c)²}=0.866L₀
The length of the rod will decrease.
The correct answer is C. The length of the rod will decrease.
According to the theory of special relativity, when an object is moving at a significant fraction of the speed of light, its length appears shorter to a stationary observer compared to its length in its own rest frame. This phenomenon is known as length contraction. As the rod is moving at a velocity equal to 1/2 the speed of light, a stationary observer will perceive its length to be shorter than its original value.
The correct answer is C) The length of the rod will decrease.
This phenomenon is known as length contraction or Lorentz contraction, which is a consequence of the theory of special relativity. According to special relativity, as an object moves closer to the speed of light, its length in the direction of motion appears to contract from the perspective of an observer at rest relative to the object.
To understand why this happens, imagine two reference frames: one where the observer is stationary and another where the rod is moving at a high velocity. In the reference frame of the stationary observer, they will perceive the rod to be shorter than its actual length. This is because as the rod moves closer to the speed of light, its internal clock slows down relative to the observer, causing time dilation. Hence, from the observer's perspective, the rod appears contracted along its direction of motion.
To calculate the exact value of the length contraction, we can use the Lorentz factor, γ, which is defined as γ = 1/√(1 - (v^2/c^2)), where v is the velocity of the rod and c is the speed of light. In this case, the velocity is 1/2 the speed of light, so v = (1/2)c. Plugging this value into the Lorentz factor equation, we can find γ. Once we have γ, we can multiply it by the rest length of the rod to obtain the observed length. In this scenario, the observed length will be less than the rest length, indicating a contraction.
So, the correct answer is C) The length of the rod will decrease.