Kinematics question centripedal acceleration and projectile motion

In summary, the conversation revolved around calculating the centripetal acceleration of a stone that flies off horizontally and strikes the ground 15m away after the string holding it 2m above the ground breaks. The process involved calculating the time it took for the stone to fall 1m using kinematics equations, then determining the necessary speed for the stone to travel 15m in that time, and finally plugging that speed into the equation for centripetal acceleration to get an answer of 249.0912 m/s^2. The participants also discussed recalculating the time to fall and confirmed that the overall process was correct.
  • #1
reb659
64
0

Homework Statement


A stone is swirled in a horizontal circle 1.00m above the ground by means of a string 2.00m long. The string breaks, and the stone files off horizontally and strikes the ground 15.0m away. What was the centripetal acceleration of the stone before the string breaks?


Homework Equations



kinematics equations

The Attempt at a Solution


First I calculated how long it took for the stone to fall 1 meter using h=1/2*g*t^2 since initial velocity is zero because its only rotating horizontally. I got a time of .672 seconds. Then I determined the speed necessary for the stone to travel 15m in this .672 seconds using d=v*t. I got v=22.32 m/s. I plugged this speed back into the equation for centripedal acceleration, v^2/r, and got an Ac of 249.0912 m/s^2.
Is this correct?
 
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  • #2
I'd start by recalculating the time to fall.
 
  • #3
Ugh, yeah, I miscalculated it. I got a new t=.452. Is the process I followed on this problem correct otherwise?
 
  • #4
reb659 said:
Ugh, yeah, I miscalculated it. I got a new t=.452. Is the process I followed on this problem correct otherwise?

Yep.

Good luck.
 

Related to Kinematics question centripedal acceleration and projectile motion

What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences as it moves in a circular path. It is always directed towards the center of the circle and is perpendicular to the object's velocity.

How is centripetal acceleration related to centripetal force?

Centripetal acceleration is directly proportional to the centripetal force acting on an object. This means that as the centripetal force increases, the centripetal acceleration also increases proportionally.

What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and is affected only by the forces of gravity and air resistance. It follows a curved path known as a parabola.

What is the difference between centripetal acceleration and tangential acceleration?

Centripetal acceleration is the acceleration towards the center of a circle, while tangential acceleration is the acceleration along the tangent of a circle. In other words, centripetal acceleration changes the direction of an object's velocity, while tangential acceleration changes the magnitude of its velocity.

How does the angle of launch affect the range of a projectile?

The angle of launch has a direct impact on the range of a projectile. The maximum range is achieved when the angle of launch is 45 degrees, as this angle produces an equal amount of vertical and horizontal displacement. Any angle above or below 45 degrees will result in a shorter range.

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