Mechanical Systems
A roundabout is pushed from rest with a constant angular acceleration of 0.36 rads-2 for 10 seconds. Calculate the angle turned by the roundabout in this time.
θ = 18 rad
A guitar string tuned to a frequency of 440 Hz is played at the same time as a guitar turned to 436 Hz. A series of beats is heard. Calculate the period between each beat.
T = 0.25 s
A battery with EMF of 12.0 , and internal resistance of 0.70 Ω is connected to a resistor of resistance 10.3 Ω. Calculate the terminal voltage of the battery.
VT = 11.2 V
A system consists of two objects with masses 3.0 kg and 5.0 kg, placed 4.0 m apart. Calculate the distance, x, of the center of mass of the system from the 3.0 kg object.
x = 2.5 m
A guitar string of length 85.0 cm is fixed between two ends. The lowest note made by the string is 255 Hz. Calculate the speed of the wave on this string.
v = 434 ms-1
A step-up transformer outside a power station has 3200 turns in its primary coil and 51200 turns in its secondary coil. The voltage across the primary coil is 25000 V. What's the voltage of the electricity supplied by the transformer?
400000 V (400 kV)
A rotating glass door picots on a central axis. A person pushes, at right angles to the stationary door, with a force of 155 N at a point 90 cm from the central axis. The push produces an angular acceleration of 0.38 rads-2. Calculate the rotational inertia of the glass door.
I = 367 kgm2
A ferry emits a long, continuous blast from its horn, as it approaches a wharf. The frequency of the ships' horn is 145 Hz but a person on the wharf records a frequency of 148 Hz. Calculate the speed of the ferry. The speed of sound is 340 ms-1.
Vs = 6.89 ms-1
An RC Circuit has a supply voltage of 25 V, a supply frequency of 50 Hz, a capacitance of 45μF (45 x 10-6 F), and a resistance of 205 Ω. Calculate the current in the circuit.
I = 0.12 A
A 0.50 kg mass attached to a vertical spring oscillates with a period of 0.80 s. Calculate the spring constant of the spring.
k = 30.8 N/m
Monochromatic light with a wavelength of 590 nm (5.90 x 10-7 m) passes through two narrow slits and forms an interference pattern on a screen, 0.95 m away from the slits as shown in the diagram above. The 2nd order bright band makes an angle of 5 with the central band. Calculate the distance between the slits being used.
d = 1.35 x 10-5 m
An LR circuit has a supply voltage of 110 V, a supply frequency of 60 Hz, a current of 0.27 A and a resistance of 350 ohms. Calculate the inductance of the circuit.
L = 0.55 H
A solid 7.0 kg cylinder of radius 12 cm, initially at rest rolls down a 0.40 m high slope without slipping. It reaches a speed of 0.90 ms-1 at the bottom of the slope. Calculate the rotational kinetic energy of the cylinder at bottom of slope.
Ek(ROT) = 24.7 J
Monochromatic light passes through a diffraction grating of 250 lines per mm. The 2nd order bright band makes an 18° angle with the zero order band. Find the frequency of the light. The speed of light is 3.0 x 108 ms-1.
f = 4.9 x 1014 Hz
An LRC circuit has an inductance of 0.3 H, a capacitance of 90 μF, and a resistance of 45 Ω. Calculate the supply frequency that will give the maximum current.
30.6 Hz