A 2.5 kg object is whirled in a vertical circle whose radius is 0.89 m. If the time of one revolution is 0.94 s, the magnitude of the tension in the string (assuming uniform speed) when it is at the top is
I just need the formula and it doesn't even have to be manipulated.
The formula you need to find the magnitude of the tension in the string when the object is at the top of the vertical circle is the centripetal force formula:
F = (m * v^2) / r
In this formula:
F represents the centripetal force,
m represents the mass of the object,
v represents the speed of the object, and
r represents the radius of the circle.
To find the speed of the object, you need to calculate it using the formula:
v = 2 * π * r / t
In this formula:
v represents the speed of the object,
π is a mathematical constant approximately equal to 3.14159,
r represents the radius of the circle, and
t represents the time of one revolution.
To find the magnitude of the tension in the string, you'll substitute the calculated speed (v) into the centripetal force formula and solve for F.
The formula for the magnitude of tension in the string when an object is at the top of a vertical circle is given by:
T = (m * v^2) / r + m * g
Where:
T is the tension in the string,
m is the mass of the object,
v is the velocity of the object,
r is the radius of the circle,
g is the acceleration due to gravity.
In this case, the mass of the object is 2.5 kg, the radius of the circle is 0.89 m, and the time of one revolution is 0.94 s.
Since we're assuming uniform speed, we can calculate the velocity using the formula:
v = (2π * r) / t
Where:
v is the velocity of the object,
r is the radius of the circle,
t is the time of one revolution.
Plugging in the values:
v = (2 * π * 0.89) / 0.94
Once you calculate the value of v, you can substitute it back into the formula for tension:
T = (2.5 * v^2) / 0.89 + (2.5 * 9.8)
Simplifying this equation will give you the magnitude of the tension in the string when the object is at the top.