# Special Relativity - Time Dilation and Length Contraction

• erok81
In summary, the question involves solving for a velocity to make a moving clock run at half the rate of one at rest and to halve the length of an object. This can be done by setting gamma equal to 2 and using the equations t' = t*gamma and L = L0/gamma, resulting in a velocity of 0.86c for both parts of the question. However, this may have been an intentional attempt to make you doubt your solution.

## Homework Statement

I have a two part question where one has to solve for a velocity to make a moving clock run half the rate as one at rest. Then the second part is what velocity would an object have to move in order to make its length halved.

## Homework Equations

$$t'=t\gamma$$

$$L=\frac{L_{0}}{\gamma}$$ where L0 is the object at rest.

$$\gamma=\frac{1}{\sqrt{1-\beta^{2}}}$$

## The Attempt at a Solution

I chose gamma to be equal to two. That way, using my equations above, the time would run slower by half and the length the same.

Is this an incorrect way of thinking for this problem? I have both problems with the same velocity, 0.86c. I thought it kind of odd that a two part question would have the same answer so I am really doubting what I've solved for.

Am I close?

You are correct. Maybe their goal was to make you second guess yourself :)

## 1. What is special relativity?

Special relativity is a fundamental theory in physics that explains the relationship between space and time. It was developed by Albert Einstein in 1905 and is based on two main principles: the laws of physics are the same for all observers in uniform motion, and the speed of light is constant in all inertial frames of reference.

## 2. What is time dilation?

Time dilation is a phenomenon predicted by special relativity where time appears to pass slower for an object in motion compared to an observer at rest. This means that time is not absolute and can be affected by an object's velocity. The faster an object moves, the slower time appears to pass for that object.

## 3. How does length contraction work?

Length contraction is another phenomenon predicted by special relativity where an object in motion appears to become shorter in the direction of its motion. This means that the length of an object is not constant and can also be affected by its velocity. The faster an object moves, the shorter it appears to be in the direction of its motion.

## 4. What is the equation for time dilation?

The equation for time dilation is t = t0 / √(1 - v^2/c^2), where t is the time experienced by the moving object, t0 is the time observed by the stationary observer, v is the velocity of the moving object, and c is the speed of light. This equation shows that as the velocity of an object approaches the speed of light, time dilation becomes more significant.

## 5. How is special relativity relevant in everyday life?

Special relativity is relevant in everyday life because it helps us understand and predict the behavior of objects moving at high speeds, such as in space travel or particle accelerators. It also plays a crucial role in technologies like GPS, which would not work accurately without taking into account the effects of time dilation on satellites in orbit.