Do mechanical engineers use a lot of math
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Hello!
a) Assuming this is asking for the minimum speed for the rock to make the full circle, we must find the minimum speed necessary for the rock to continue moving in a circular path when it's at the top of the circle.
At the top of the circle, we have:
- Force of gravity (downward)
*Although the rock is still connected to the string, if the rock is swinging at the minimum speed required, there will be no tension in the string.
Therefore, only the force of gravity produces the net centripetal force:
We can simplify and rearrange the equation to solve for 'v'.
Plugging in values:
b)
Let's do a summation of forces at the bottom of the swing. We have:
- Force due to gravity (downward, -)
- Tension force (upward, +)
The sum of these forces produces a centripetal force, upward (+).
Rearranging for 'T":
Plugging in the appropriate values:
Answer:
distance = 6.1022 x10^16[m]
Explanation:
To solve this problem we must use the formula of the average speed which relates distance to time, so we have
v = distance / time
where:
v = velocity = 3 x 10^8 [m/s]
distance = x [meters]
time = 6.45 [light years]
Now we have to convert from light-years to seconds in order to get the distance in meters.
Now using the formula:
distance = v * time
distance = (3*10^8)*203407200
distance = 6.1022 x10^16[m]