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2 answers:
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(a) Centripetal: , tangential:
The radius of the track (which is the distance of the car from the centre of the circular path) is
r = 0.30 km = 300 m
The angular acceleration is
We can find the angular velocity of the car after half of a lap using the equivalent of the SUVAT equation for rotational motions:
where
since the car starts from rest
is the angular displacement after half a lap
Solving for ,
Now we can find the centripetal acceleration with the formula:
while the tangential acceleration is simply given by
(b) The mass of the car is not given, so it is not possible to find the forces.
1) Yes, it is a conservative force
2) The potential energy at (5m, 5m) is 20 J
Explanation:
1)
A force is defined to be conservative if the work done by the force when moving an object does not depend on the path taken, but only on the initial and final position of the object.
Let's verify if this condition is met for the force in this problem:
- For going from (0 m, 0 m) to (5 m, 5 m), the work done is 20 J (A)
Then we can go from (0 m, 0 m) to (5 m, 5 m) through a different path:
- from (0 m, 0 m) to (5 m, 0 m) (work done: 25 J)
- from (5 m, 0 m) to (5 m, 5 m) (work done: -5 J)
Total work done in the second path: 25 J + (-5 J) = 20 J --> same as (A)
We can also go from (0 m, 0 m) to (5 m, 5 m) through a different path:
- from (0 m, 0 m) to (0 m, 5 m) (work done: 35 J)
- from (0 m, 5 m) to (5 m, 5 m) (work done: -15 J)
Total work done in the third path: 35 J + (-15 J) = 20 J --> same as (A)
So, the force is conservative, since the work done does not depend on the path taken.
2)
For a conservative force, the change in potential energy of the object moved by the force is equal to the work done by the force in moving the object from A to B.
Here have:
Point A: (0m, 0m)
Point B: (5m, 5m)
So, the change in potential energy is equal to the work done from A to B:
where
is the potential energy in point B
is the potential energy in point A
In this problem, the potential energy at the origin (point A) is zero, so
Also we know that the work done is
W = 20 J
So, we find
Learn more about potential energy:
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