Answer:
(a): a = 0.4m/s²
(b): α = 8 radians/s²
Explanation:
First we propose an equation to determine the linear acceleration and an equation to determine the space traveled in the ramp (5m):
a= (Vf-Vi)/t = (2m/s)/t
a: linear acceleration.
Vf: speed at the end of the ramp.
Vi: speed at the beginning of the ramp (zero).
d= (1/2)×a×t² = 5m
d: distance of the ramp (5m).
We replace the first equation in the second to determine the travel time on the ramp:
d = 5m = (1/2)×( (2m/s)/t)×t² = (1m/s)×t ⇒ t = 5s
And the linear acceleration will be:
a = (2m/s)/5s = 0.4m/s²
Now we determine the perimeter of the cylinder to know the linear distance traveled on the ramp in a revolution:
perimeter = π×diameter = π×0.1m = 0.3142m
To determine the angular acceleration we divide the linear acceleration by the radius of the cylinder:
α = (0.4m/s²)/(0.05m) = 8 radians/s²
α: angular aceleration.
Albert Einstein came up with the theory of general relativity to explain the law of gravity, whilst Newton's three laws of gravity is universal. To understand this further, it's best to understand it in scientific terms.
The weird thing about science is that words that are used in a colloquial sense may have a completely opposite definition in scientific terms.
A law in science is a constant and invariable statement that is universal. Wherever you may be in the universe, Newton's three laws of gravity will always be applied.
The word "theory" doesn't imply conjecture or an idea someone made up after a night of drinking. In science, a theory is the highest level of certainty behind mathematical proof -- which isn't even a part of science, obviously. A theory has to be substantiated by all available evidence and contradicted by none. All theories also have to have to be falsifiable. For this reason, theories can never be proven. Einstein's theory of general relativity has great predictive power, but in some cases, the predictions aren't always constant. Theories are often revised to fit new available evidence.
I am using the equation F=ma (force equals mass times acceleration) to solve these problems.
1. You are looking for force, and have mass and acceleration. You just plug in the values for mass and acceleration to get the force needed.
F=(15kg)(5m/s^2)
F=75N
2. Again, you are looking for force, and just need to plug in the values for mass and acceleration
F=(3kg)(2.4m/s^2)
F=7.2N
3. In this problem, you have force and mass, but need to find acceleration. To do this, you need to get acceleration alone on one side of the equation - divide each side by m. Your equation will now be F/m=a
a=(5N)/(3.7kg)
a=18.5m/s^2
I did not use significant figures. Let me know if you need to do that and need any help on that. Hope this helps!
Answer:
5.08*10^{-13}N
Explanation:
With this information we can calculate the velocity of the proton by taking into account the kinetic energy of the proton:
The magnitude of the magnetic force will be:
hope this helps!
