In an auditorium, a physics teacher uses a pendulum made by hanging a bowling ball from a wire to the ceiling. At the low point in its swing, a ball with a mass of 7.2-kg has a speed of 6 m/s. Ignoring air resistance, how high will the bob swing above the low point before reversing direction?
My book and slides from professor do not address pendulums! How do I start this?
The KE at the bottom is equal to the max PE at the top.
1/2 m v^2=mgh
h= .5 (6^2)/9.8 meters
the kinetic energy of the bob becomes gravitational potential energy
1/2 * m * v^2 = m * g * h
1/2(7.2)(6^2)=7.2(9.8)h
h=1.8
To solve this problem, you can use the principle of conservation of mechanical energy. In the absence of air resistance, the total mechanical energy of the pendulum remains constant throughout its motion.
The mechanical energy of a pendulum consists of two components: kinetic energy (KE) and potential energy (PE). The kinetic energy is due to the motion of the ball, and the potential energy is due to its position above the low point.
At the low point of the pendulum swing, all the potential energy is converted into kinetic energy. This means that:
PE(low point) = 0
At the highest point of the swing, all the kinetic energy is converted into potential energy. This means that:
KE(highest point) = 0
Since energy is conserved, the total mechanical energy (E) of the pendulum is the same at both the low and high points:
E(low point) = E(highest point)
Now we can use the kinetic energy equation and potential energy equation to solve for the height above the low point:
KE = 0.5 * mass * velocity^2
PE = mass * gravitational acceleration * height
At the low point, the entire energy is kinetic, so we have:
E(low point) = KE(low point) = 0.5 * mass * velocity^2
At the highest point, the entire energy is potential, so we have:
E(highest point) = PE(highest point) = mass * gravitational acceleration * height
Since the total mechanical energy is conserved, we can equate the two equations:
0.5 * mass * velocity^2 = mass * gravitational acceleration * height
Now we can solve for the height above the low point (height):
height = (0.5 * mass * velocity^2) / (mass * gravitational acceleration)
height = (0.5 * 7.2 kg * (6 m/s)^2) / (7.2 kg * 9.8 m/s^2)
height = (0.5 * 36 m^2/s^2) / 70.56 m^2/s^2
height = 18 m^2/s^2 / 70.56 m^2/s^2
height ≈ 0.255 m
Therefore, the bob will swing approximately 0.255 meters above the low point before reversing direction.