Practise Edexcel A-Level Physics AS and A2 mathematical skills by handling uncertainties, units, formula substitutions, speeds and graphs.
A student investigated the flow of water through a horizontal pipe using the apparatus shown.
The mass M of water leaving the pipe in a time t is given by the formula
where
density of water
P= pressure difference between the ends of the pipe
r= internal radius of the pipe
viscosity of water
L= distance between digital pressure gauges
Show that the formula gives the unit for as .
A student investigated the properties of a spring using the apparatus shown.
The student determined the time period T of the oscillations of the mass-spring system.
The student displaced the mass downwards. He released the mass so that the mass oscillated vertically. He used a stopwatch to measure the time for multiple oscillations.
The student recorded the following results.
Calculate the mean value of T.
Mean value of T =
An L-shaped steel rod was held horizontally in a stand clamped by its shorter end as shown.
The end of the steel rod was at a height p above the bench. A student attached a mass m to the end of the steel rod causing it to bend towards the bench. The end of the steel rod was then at a height q above the bench.
The difference between p and q was recorded as 26 mm ± 1 mm.
Explain why the uncertainty in this value is given as 1 mm.
The shear modulus G is a measure of a material’s resistance to bending, and is given by
G = 32mglx²/(πyd⁴)
where m is the mass attached to the end of the rod and y is the vertical deflection. l and x are the lengths as shown below.
Determine a value of G for steel in N m^-2.
m = 100 g with negligible uncertainty
l = 58.9 cm ± 0.1 cm
x = 10.3 cm ± 0.1 cm
y = 26 mm ± 1 mm
G =
A student investigated the damped oscillations of a pendulum using the apparatus shown.
The paper cone acted as a damper.
The student displaced the cone and allowed the pendulum to oscillate.
He measured the amplitude A every 5 oscillations and recorded the value to the nearest 5 mm.
The relationship between A and the number of oscillations n is
A=A_0 e^- n
where A_0 is the initial amplitude and is a constant.
Determine the value of A_0 from the graph.
A_0=