When you put water in a kitchen blender, it begins to travel in a 7-cm-radius circle at a speed of 1 m/s. How quickly is the water accelerating?
what is v^2/r ?
To determine the acceleration of the water in the blender, we can use the formulas for centripetal acceleration.
The centripetal acceleration (a) can be calculated using the formula:
a = (v^2) / r
Where:
v is the velocity of the water (1 m/s), and
r is the radius of the circular path (7 cm or 0.07 m).
Substituting the given values, we can calculate the acceleration:
a = (1^2) / 0.07
a = 1 / 0.07
a ≈ 14.29 m/s^2
Therefore, the water in the blender is accelerating at approximately 14.29 m/s^2.
To determine the acceleration of the water in the blender, we need to find the magnitude of the centripetal acceleration. The centripetal acceleration is given by the formula:
a = v^2 / r
where:
- a is the centripetal acceleration
- v is the speed of the water
- r is the radius of the circular path
In this case, the speed of the water is given as 1 m/s and the radius of the circle it travels in is 7 cm. However, to use the formula, we need the radius in meters:
r = 7 cm = 7/100 m = 0.07 m
Now we can substitute the values into the formula:
a = (1 m/s)^2 / 0.07 m
= 1 m^2/s^2 / 0.07 m
≈ 14.29 m/s^2
Therefore, the water in the blender is accelerating at a rate of approximately 14.29 m/s^2.