A stone is tied to a string (length = 0.450 m) and whirled in a circle at the same constant speed in two different ways. First, the circle is horizontal and the string is nearly parallel to the ground. Next, the circle is vertical. In the vertical case the maximum tension in the string is 18.0% larger than the tension that exists when the circle is horizontal. Determine the speed of the stone.

Question

A stone is tied to a string (length = 0.450 m) and whirled in a circle at the same constant speed in two different ways. First, the circle is horizontal and the string is nearly parallel to the ground. Next, the circle is vertical. In the vertical case the maximum tension in the string is 18.0% larger than the tension that exists when the circle is horizontal. Determine the speed of the stone.

Answer 1

mg+mv^2/r = 1.18(mv^2/r)

this should solve it, solve for v.

mg=.18mv^2/r
v= sqrt(r*g*.18)

Answer 2

oops,

v= sqrt rg/.18

check that.

Answer 3

what is the radius? how do we find that out

Answer 4

To determine the speed of the stone, we can start by finding the tension in the string when the circle is horizontal. Let's denote this tension as T_horizontal.

In the horizontal case, the stone is moving in a circle with a certain centripetal force, directed towards the center of the circle. This force is provided by the tension in the string.

Using Newton's second law of motion, we can set up the following equation:

T_horizontal = (m * v^2) / r,

where T_horizontal is the tension in the string, m is the mass of the stone, v is the speed of the stone, and r is the radius of the circular path.

Now, let's consider the vertical case. In this case, the maximum tension in the string is 18.0% larger than T_horizontal. Hence,

T_vertical = T_horizontal + 0.18 * T_horizontal.

Simplifying this equation, we get:

T_vertical = 1.18 * T_horizontal.

We know that the radius of the circular path remains the same in both cases. Therefore, for the vertical case, the centripetal force is provided by the tension in the string, given by T_vertical.

Again using Newton's second law of motion, we can set up the following equation:

T_vertical = (m * v^2) / r.

Now, we can substitute the value of T_vertical from the previous equation:

1.18 * T_horizontal = (m * v^2) / r.

Rearrange the equation to solve for v:

v^2 = (1.18 * T_horizontal * r) / m.

Taking the square root of both sides of the equation, we get:

v = √((1.18 * T_horizontal * r) / m).

Now, we have an expression for the speed of the stone in terms of T_horizontal, r, and m.

To find the speed of the stone, we need to know the values of T_horizontal, r, and m. Once we have these values, we can substitute them into the equation and calculate the speed.