IB Physics SL S2.1 Exploring and Designing Topic Practice

A student investigates whether the Stefan-Boltzmann law, $L=4 \pi \sigma R^{2} T^{4}$, applies to stars.
L= luminosity of the star, in W
$\sigma=$ Stefan-Boltzmann constant
R= radius of the star, in m
T= surface temperature of the star, in K
To verify the law, they obtain values from databases and manipulate the data as shown.

Suggest a possible improvement of the investigation, related to the range of the surface temperatures of the stars selected.

A group of students uses pressurized air to move a piston that forces a nail into a block of wood. A gauge is used to measure the pressure P of compressed air above atmospheric pressure. The nail enters the wood perpendicular to its surface.

The students use a ruler to measure the length of the nail which remains above the surface of the wood as shown. The depth of the nail inside the wood is d. All necessary length measurements are recorded using a ruler with uncertainty $\pm 1 \mathrm{~mm}$.

The students systematically increase the pressure and calculate d.

State one variable that needs to be controlled when collecting the data.

A student studies the relationship between the centripetal force applied to an object undergoing circular motion and its period T.
The object (mass m ) is attached by a light inextensible string, through a tube, to a weight W which hangs vertically. The string is free to move through the tube. A student swings the mass in a horizontal, circular path, adjusting the period T of the motion until the radius r is constant. The radius of the circle and the mass of the object are measured and remain constant for the entire experiment.

The student collects the measurements of T five times, for weight W. The weight is then doubled ( 2 W ) and the data collection repeated. Then it is repeated with 3 W and 4 W. The results are expected to support the relationship

State why the experiment is repeated with different values of W.

In reality, there is friction in the system, so in this case W is less than the total centripetal force in the system. A suitable graph is plotted to determine the value of m r experimentally. The value of m r was also calculated directly from the measured values of m and r.