Radial Acceleration on a string

In summary: I’m still confused, where is the cos coming in from?The cos comes in from the equation for the tangential velocity.
  • #1
alexi_b
49
1

Homework Statement


A ball on the end of a string is whirled around in a horizontal circle of radius 0.250m. The plane of the circle is 1.06m above the ground. The string breaks and the ball lands 1.90m (horizontally) away from the point on the ground directly beneath the ball's location when the string breaks. Calculate the radial acceleration of the ball during its circular motion.

Homework Equations


Ar = -Ac = v^2/r

The Attempt at a Solution


I see no relevance between the last two measurements and only the radius is of use, but obviously they come into play somehow. I don't know where to begin with this so any help would be appreciated!
 
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  • #2
Use projectile motion equations for after the string breaks with ##v_0=v## and ##\theta=0##, where ##v## the tangential velocity the moment the string breaks
You should be able to calculate ##v_0## using projectile motion equations and the data given by the problem. Then you just plug this ##v_0=v## into the equation you have wrote in part 2. Homework Equations .
 
Last edited:
  • #3
Delta² said:
Use projectile motion equations for after the string breaks with ##v_0=v## and ##\theta=0##, where ##v## the tangential velocity the moment the string breaks
You should be able to calculate ##v_0## using projectile motion equations and the data given by the problem. Then you just plug this ##v_0=v## into the equation you have wrote in part 2. Homework Equations .
If theta is equal to zero won’t the whole top part of the equation be 0 as well? And then would mean I couldn’t solve for the Vo
 
  • #4
alexi_b said:
If theta is equal to zero won’t the whole top part of the equation be 0 as well? And then would mean I couldn’t solve for the Vo
if theta is 0, that only means that ##V_{0y}=0## and ##V_{0x}=V_0\cos0=V_0##
 
  • #5
Delta² said:
if theta is 0, that only means that ##V_{0y}=0## and ##V_{0x}=V_0\cos0=V_0##
I’m still confused, where is the cos coming in from?
 

Related to Radial Acceleration on a string

What is radial acceleration on a string?

Radial acceleration on a string is the acceleration experienced by an object moving in a circular path while attached to a string. It is the rate of change of the object's velocity as it moves along the circular path.

How is radial acceleration calculated?

Radial acceleration can be calculated using the formula a = v^2/r, where a is the radial acceleration, v is the object's velocity, and r is the radius of the circular path.

How does the radius of the circular path affect radial acceleration?

The radius of the circular path has a direct effect on the magnitude of the radial acceleration. A smaller radius will result in a larger radial acceleration, while a larger radius will result in a smaller radial acceleration.

What is the relationship between radial acceleration and tangential acceleration?

Radial acceleration and tangential acceleration are perpendicular to each other. As an object moves along a circular path, its velocity is constantly changing in both magnitude and direction. Radial acceleration is responsible for the change in direction, while tangential acceleration is responsible for the change in magnitude of the velocity.

How does radial acceleration affect an object's motion?

Radial acceleration causes an object to constantly change its direction of motion as it moves along a circular path. This results in circular motion or circular acceleration, which is characterized by a constant change in direction but a constant speed.

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