A ping pong ball is rolling across a table at 2.1 cm/s. When the ball is 1.32 m away from the edge your little brother starts to blow on it. If the little doofus hopes to prevent the ball from falling off the edge, what minimum acceleration must be achieved?
To determine the minimum acceleration required to prevent the ping pong ball from falling off the edge of the table, we can use the principles of motion.
First, let's understand the situation given in the problem. The ping pong ball is already rolling across the table at a constant speed of 2.1 cm/s. Your little brother starts blowing on it when the ball is 1.32 m away from the edge.
To calculate the minimum acceleration required, we can use the kinematic equation:
vf^2 = vi^2 + 2ad
Where:
- vf is the final velocity (which should be zero if the ball is to be prevented from falling off the edge)
- vi is the initial velocity of the ball (2.1 cm/s)
- a is the acceleration we want to find
- d is the distance traveled by the ball (1.32 m)
Since we want the ball to stop, the final velocity should be zero. Therefore, the equation becomes:
0 = (2.1 cm/s)^2 + 2a(1.32 m)
Next, we need to convert the units to be consistent. Let's convert centimeters to meters:
0 = (0.021 m/s)^2 + 2a(1.32 m)
Now, rearranging the equation to solve for acceleration (a):
2a(1.32 m) = - (0.021 m/s)^2
a = - ((0.021 m/s)^2) / (2 * 1.32 m)
a ≈ - 0.000154 m/s^2
The minimum acceleration required to prevent the ping pong ball from falling off the edge is approximately -0.000154 m/s^2. The negative sign indicates that the acceleration should act in the opposite direction of the ball's initial motion.