A wire is frictionless between points A and B and rough between B and C. A is 5m above the ground, B is zero, and C is 2m above the ground. The 0.400kg bead starts from rest at A. If the bead comes to rest at C, find the loss in mechanical energy as it goes from B to C.
I can't figure out how to find mechanical energy and can't even find an equation in my book.
To find the loss in mechanical energy as the bead goes from B to C, we need to calculate the initial and final mechanical energies of the bead and then find their difference.
Mechanical energy (E) is the sum of the potential energy (PE) and the kinetic energy (KE) of an object.
The potential energy (PE) of an object is given by the equation: PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above a reference point.
The kinetic energy (KE) of an object is given by the equation: KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
Given:
- Mass of the bead, m = 0.400 kg
- Height of A above the ground, h_A = 5 m
- Height of C above the ground, h_C = 2 m
To find the initial mechanical energy at point A, we need to calculate the potential energy:
PE_A = m * g * h_A, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
To find the final mechanical energy at point C, we need to calculate both the potential energy and kinetic energy at point C:
PE_C = m * g * h_C
KE_C = 0, since the bead comes to rest at point C.
Now we can calculate the loss in mechanical energy as the difference between the initial and final mechanical energies:
Loss in mechanical energy = (PE_A - PE_C) + (KE_A - KE_C)
Since the bead starts from rest at point A, its initial kinetic energy (KE_A) is also 0.
Loss in mechanical energy = PE_A - PE_C
Now you can substitute the given values into the equations to find the loss in mechanical energy as the bead goes from B to C.