a green bead of mass 70 g slides along a straight wire. The length of the wire from point "A" to point "B" is 0.700 m, and point "A" is 0.400 m higher than point "B". A constant friction force of magnitude 0.020 0 N acts on the bead. If the bead is released from rest at point "A", what is its speed at point "B" ?
To find the speed of the bead at point B, we can use the principle of conservation of mechanical energy. This principle states that the total mechanical energy of a system remains constant as long as only conservative forces are present.
In this case, the only force acting on the bead is friction, which is a conservative force. Therefore, we can use the conservation of mechanical energy to solve the problem.
The mechanical energy of the bead consists of its kinetic energy and potential energy. At point A, the bead has no kinetic energy but has potential energy due to its height above point B. At point B, the bead has no potential energy but has kinetic energy due to its motion.
The potential energy of the bead at point A is given by the equation:
Potential energy at A = mass * gravity * height
= (70 g) * (9.8 m/s^2) * (0.400 m)
The kinetic energy of the bead at point B is given by the equation:
Kinetic energy at B = 1/2 * mass * (velocity at B)^2
Since mechanical energy is conserved, we can equate the potential energy at A to the kinetic energy at B:
Potential energy at A = kinetic energy at B
(70 g) * (9.8 m/s^2) * (0.400 m) = 1/2 * (70 g) * (velocity at B)^2
Simplifying this equation, we can solve for the velocity at B:
(70 g) * (9.8 m/s^2) * (0.400 m) = 1/2 * (70 g) * (velocity at B)^2
Solving for velocity at B:
(9.8 m/s^2) * (0.400 m) = 1/2 * (velocity at B)^2
3.92 m^2/s^2 = 1/2 * (velocity at B)^2
Velocity at B = √(2 * 3.92 m^2/s^2)
Velocity at B = √7.84 m^2/s^2
Velocity at B ≈ 2.8 m/s
Therefore, the speed of the bead at point B is approximately 2.8 m/s.