1. A body moving through the air at a speed v, experience a retarding force f, given by f= KAPv-square where A is the surface area of the body, p is the density of air and K is a numericalconstant.
find the value of × and d expression of f.
2. A particle of mass M attached to a string of Length r is whirsted round in a circle with a speed U..
find the form of the expression for the tension in the string?
To find the value of × in the expression for the retarding force f= KAPv^2, we need more information or clarification. It seems that a variable or a value might be missing.
However, I can explain how to derive the expression for the retarding force. The retarding force experienced by a body moving through a fluid like air can be determined using fluid dynamics principles.
The drag force, or retarding force, experienced by an object in a fluid depends on several factors, including the surface area of the object (A), the density of the fluid (p), the velocity of the object (v), and the coefficient of drag (K). The coefficient of drag depends on the shape and properties of the object.
The general expression for the drag force is given by f = KAPv^2, where:
- f is the retarding force or drag force.
- K is a numerical constant related to the shape and properties of the object.
- A is the surface area of the object perpendicular to the direction of motion.
- p is the density of the fluid, in this case, the density of air.
- v is the velocity of the object through the fluid.
The specific value of the coefficient K and further information are required to determine the exact value of × and to simplify the expression further.
Regarding the question about the tension in the string for a particle of mass M whirling around in a circle with a speed U, the tension can be determined using the centripetal force concept.
In circular motion, the centripetal force required to keep an object moving in a circle is given by F = (M * U^2) / r, where:
- F is the centripetal force.
- M is the mass of the object.
- U is the speed of the object in circular motion.
- r is the radius or length of the string.
The tension in the string is equal to the centripetal force, so the expression for the tension in the string will be T = (M * U^2) / r.
Remember to use appropriate units and ensure that all the values are consistent in the equations.