Q5-57E - University Physics with Modern Physics

Question

You tie a cord to a pail of water and swing the pail in a vertical circle of radius $0.600\text{\hspace{0.17em}m}$. What minimum speed must you give the pail at the highest point of the circle to avoid spilling water?

Step-by-Step Solution

Answer

The minimum speed you give the pail at the highest point is, $2.42\text{\hspace{0.17em}m/s}$. 

Step 1: Identification of the given data

The given data can be listed below as,

• The radius of the vertical circle is,$r=0.600\text{\hspace{0.17em}m}$ .

Step 2: Significance of centripetal force

The centripetal force occurs when an object moving in a circular motion, it pulls or pushes an object toward the center of a circle.

Step 3: Determination of minimum speed you give the pail

The expression for the centripetal force can be expressed as,

 $F=\frac{m{v}^2}{r}$

Here $m$ is the mass,$v$ is the velocity, and $r$ is the radius.

 

Substitute $mg$ for in $F$ the above equation.

 $\begin{array}{c}mg=\frac{m{v}^2}{r}\\ v=\sqrt{gr}\end{array}$

Here $g$ is the acceleration due to gravity.

 

Substitute for $9.8{\text{\hspace{0.17em}m/s}}^{\text{2}}$ for,$g$ and $0.600\text{\hspace{0.17em}m}$ for $r$ in the above equation.

 $\begin{array}{c}v=\sqrt{9.8{\text{\hspace{0.17em}m/s}}^{\text{2}}\times 0.600\text{\hspace{0.17em}m}}\\ =2.42\text{\hspace{0.17em}m/s}\end{array}$

Hence, the required minimum speed is,$2.42\text{\hspace{0.17em}m/s}$ .