Two identical racing horses go around a semicircular turn in a racecourse. The horses have the same speed, but horse A is on the inner side while horse B is on the outer side of the circular turn. Which horse has the greater acceleration while in the turn?
Acceleration is indirectly proportional to radius.
a = v^2 / r
Let Horse A = r;
r = 1 = v;
a = 1.
Let B = 2r;
r = 2; v = 1;
a = 1/4
The acceleration of Horse A is much greater then Horse B.
To determine which horse has the greater acceleration while in the turn, we need to consider the concept of centripetal acceleration.
Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always points towards the center of the circle and is given by the formula:
a = (v^2) / r
Where:
- a is the centripetal acceleration
- v is the velocity of the object
- r is the radius of the circular path
In this scenario, both horses have the same speed but are on different sides of the circular turn. Since the horses are identical and have the same speed, their velocities (v) are the same as well.
However, the radius (r) of the circular path is different for each horse. Horse A, located on the inner side of the turn, has a smaller radius compared to horse B, which is on the outer side of the turn.
According to the centripetal acceleration formula, since the velocity (v) is the same for both horses, the horse with the smaller radius (r) will have the greater acceleration (a). Therefore, horse A, on the inner side of the turn, will have the greater acceleration while in the turn.