The apparatus above is used to study conservation of mechanical energy. A spring of force constant 40N/m is held horizontal over a horizontal air track, with one end attached to the air track. A light string is attached to the other end of the spring and connects it to a glider of mass m. The glider is pulled to stretch the spring an amount x from equilibrium and then released. Before reaching the photogate, the glider attains its maximum speed and the string becomes slack. The photogate measures the time t that it takes the small block on top of the glider to pass through. Information about the distance x and the speed v of the glider as it passes through the photogate are given below.
(a) Assuming no energy is lost, write the equation for conservation of mechanical energy that would apply to this situation.
(b) On the grid below, plot v2 versus x2. Label the axes, including units and scale.
(c)
i. Draw a best-fit straight line through the data.
ii. Use the best-fit line to obtain the mass m of the glider.
(d) The track is now tilted at an angle θ as shown below. When the spring is unstretched, the center of the glider is a height h above the photogate. The experiment is repeated with a variety of values of x.
Assuming no energy is lost, write the new equation for conservation of mechanical energy that would apply to this situation starting from position A and ending at position B.
