An object has a total energy that is two times its rest energy. What is its speed? Give answer in c.
what equation do i use to solve this? step by step anyone?
total energy=sqrt{(m0 c^2)^2 +(pc)^2)
and that is equal to 2mo c^2
4(mo c^2)^2=(mo c^2)^2 + (pc)^2
or (pc)^2=3( mo c^2)^2
or momentum p^2=(mo c^2) 3
or momentum p= mo c sqrt3
now, a particle of velocity v, has a momentum of mo/(sqrt(1-(v/c)^2) * v
so mo v/(factor)= mo c sqrt 3
or v= c*sqrt3*(sqrt(1-(v/c)^2)
v^2=3c^2 (1-(v/c)^2)
v^2(1+3)=3c^2
v= 3/4 c
check all that.
To solve this problem, you can use Einstein's famous equation, E = mc², which relates an object's energy (E) to its mass (m) and the speed of light (c). Here are the step-by-step instructions to find the speed of the object:
Step 1: Start with the given information that the total energy of the object is two times its rest energy. Mathematically, we can express this as:
E = 2mc², where E is the total energy and mc² is the rest energy.
Step 2: Since we are looking to find the speed of the object, we need to solve for the variable "c" in the equation. To do this, we need to isolate "c" in the expression.
Step 3: Divide both sides of the equation by 2m to isolate c²:
E / (2m) = c²
Step 4: Take the square root of both sides of the equation to solve for c:
√(E / (2m)) = c
Step 5: Finally, simplify the expression if possible and substitute the values for E (total energy) and m (mass) to find the speed of the object. Make sure to express the answer in terms of the speed of light, c.
Following these steps, you should be able to find the speed of the object.