Question

Background In this lab, we will have a mass attached to a string that hangs over a (massless, frictionless) pulley. The other end of the string is attached to a cart on an air track. An air track is like a one-dimensional air-hockey table: it ejects air in order to minimize friction. In maintaining a nearly frictionless environment, we have isolated our system (to a high degree of precision), meaning energy will be conserved. 1 Schematically, the system is hooked up as follows: Glider (mass M V Pulley String - Hanging Mass (m) Air Track mga v Recall that PE = mgh, so APE = mgAh. Noting that Ah= -Ax, we have: APE= -mgAz Or, more concisely, since "zero potential energy" is arbitrary, we simply assert: PE = -mgx For kinetic energy, we have simply: Ke=žmo? +Mv = 3(m + M)u? The law of conservation of energy states that: Etotal(t) = Etotal,initial

There are two graphs that needs to be made in this lab:

1. Total Energy Vs time with m = 20g

2. Total Energy Vs time with m = 40g

A) Explain the nature of the plots .(Linear or non linear?) The expected slope is zero in both cases. Why? Explain with the use of law of conservation of energy. What is the significance of the intercept?

B) Suppose you drew the Kinetic Energy Vs potential Energy graph: The expected slope would be -1. Why? Explain with the use of law of conservation of energy. What is the significance of the intercept?

C) Suppose you drew the Velocity Vs time graph. What would be the slope? Why? (it may help to solve for the acceleration of the system) --> Hint: a = (mg)/(M+m).

Answer 1

Solution : a total I the total energy will remain. same becauce to as the mass. Come clown the potential energy will be converted to kinetic energy that is part of total energy only so total energy remain same * linear graph * slope is zero P.EL (B ) the since Kię loss In P { = gain In Kię they are equal so slope s =-ARE --| DKE the Intercept Change In will kinetic give us & potential energy

the Velocity will encrease with time and slope as equal tre acceleration a a = mg [M7m] acceleration is rate of change of os Ált velocity DU