Lolagoeslala said:Homework Statement
A 1.01 kg mass is attached to a spring of force constant 9.5 N/cm and placed on a frictionless surface. By how much will the spring stretch if the mass moves along a circular path of radius 0.485 m at a rate of 2.14 revolutions per second?
What i was thinking was using the following equation:
Fc= Kx - mg
Which would turn into
a=kx-g
(4pi^2(R)(F)^2 +g)/K=x
ehild said:Is it a horizontal surface the mass moves on?
ehild
ehild said:I guess the surfaceis horizontal, the angle of inclination would be stated otherwise. So the only force in the plane of motion is the force of the spring. Gravity cancels with the normal force of the surface.
ehild
ehild said:Mg is a vertical force. The object moves horizontally, along a circle. What force is needed to make it move along that circle of radius 0.485 m with 2.14 revolutions per second?
ehild
The relationship between circular motion and Hooke's Law is that Hooke's Law can be applied to objects undergoing circular motion, as long as the object is attached to a spring or elastic material. The force exerted by the spring follows Hooke's Law, which states that the force is directly proportional to the displacement of the object from its equilibrium position.
Hooke's Law affects circular motion by providing a restoring force that brings the object back to its equilibrium position when it is displaced. This force allows the object to maintain its circular motion by constantly changing the direction of its velocity.
Centripetal force is the force that keeps an object moving in a circular path. In the case of circular motion and Hooke's Law, the centripetal force is provided by the spring or elastic material, as it constantly pulls the object back towards the center of the circular path.
Hooke's Law can be applied to any type of circular motion as long as the object is attached to a spring or elastic material. This includes horizontal, vertical, and inclined circular motion.
The mixture of circular motion and Hooke's Law has various practical applications, such as in the design of springs for shock absorbers, pendulums, and even roller coasters. It is also used in physics experiments to study the relationship between force, displacement, and circular motion.