Question

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?

Answer 1

The speed of the object attached to a massless rod when the rod reaches horizontal can be calculated using the principle of conservation of energy, equating initial potential energy to final kinetic energy and solving for the velocity.

Step-by-step explanation:

The student's question involves finding the speed of an object attached to a massless rod that is pivoted at one end and released from a vertical position. This is a problem in physics that falls under the topic of rotational motion and can be solved using the conservation of energy principle. The initial potential energy of the system (when the rod is vertical) will be converted to kinetic energy when the rod reaches the horizontal position.

At the initial position, we have only gravitational potential energy given by U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height which is equal to the length of the rod since the rod is vertical. When the rod is horizontal, all of this energy will have been converted to kinetic energy of the object (assuming no other forces such as air resistance), which can be calculated using KE = 0.5mv^2, where v is the velocity that we wish to find. By setting the initial potential energy equal to the final kinetic energy and solving for v, we can find the speed of the object.

Answer 2

1.40071 m/s

Step-by-step explanation:

m = Mass of object = 100 g

v = Velocity of object

h = Height of drop = 10 cm

g = Acceleration due to gravity = 9.81 m/s²

Here, the loss of potential energy is equal to the gain in kinetic energy as energy is conserved

`mgh=(1)/(2)mv^2\\\Rightarrow gh=(1)/(2)v^2\\\Rightarrow v^2=2gh\\\Rightarrow v=√(2gh)\\\Rightarrow v=√(2* 9.81* 0.1)\\\Rightarrow v=1.40071\ m/s`

The speed of the object at the instant that the rod is horizontal is 1.40071 m/s