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stevensquad1379
13.04.2020 •
Physics
The bigclaw snapping shrimp shown in (Figure 1) is aptly named--it has one big claw that snaps shut with remarkable speed. The part of the claw that moves rotates through a 90∘ angle in 1.3 ms. We assume that the claw is 1.5 cm long and that it undergoes a constant angular acceleration. (you don't need figure to solve problem)
1. What is the angular acceleration? Assume the claw starts from rest.
Express your answer in radians per second squared.
2. What is the final angular speed of the claw?
Express your answer in radians per second.
3. What is the tangential acceleration of the tip of the claw?
Express your answer with the appropriate units.
4. How fast is the tip of the claw moving at the end of its motion?
Express your answer with the appropriate units.
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Ответ:
1)![1.86\cdot 10^6 rad/s^2](/tpl/images/0596/6485/9ccfc.png)
2) 2418 rad/s
3)![27000 m/s^2](/tpl/images/0596/6485/d88d8.png)
4) 36.3 m/s
Explanation:
1)
The angular acceleration of an object in rotation is the rate of change of angular velocity.
It can be calculated using the following suvat equation for angular motion:
where:
t is the time
In this problem we have:
t = 1.3 ms = 0.0013 s is the time elapsed
Solving for
, we find:
2)
For an object in accelerated rotational motion, the final angular speed can be found by using another suvat equation:
where
t is the time
In this problem we have:
t = 1.3 ms = 0.0013 s is the time elapsed
Therefore, the final angular speed is:
3)
The tangential acceleration is related to the angular acceleration by the following formula:
where
r is the distance of the point from the centre of rotation
Here we want to find the tangential acceleration of the tip of the claw, so:
r = 1.5 cm = 0.015 m is the distance of the tip of the claw from the axis of rotation
Substituting,
4)
Since the tip of the claw is moving by uniformly accelerated motion, we can find its final speed using the suvat equation:
where
u is the initial linear speed
a is the tangential acceleration
t is the time elapsed
Here we have:
u = 0 m/s (it starts from rest)
t = 1.3 ms = 0.0013 s is the time elapsed
Substituting,
Ответ:
When I was thirteen years old, we left our hometown for the last time. I was forced to start high school in a strange place. It was hard, but I learned that being thrown into a new environment can be great.
Explanation:
It eez what it eez