Live practice

For y=2.0cos[2π(10t−0.0080x+0.35)] with x,y in cm, find phase differences for separations \(4.0\,\mathrm{m}\), \(0.50\,\mathrm{m}\), λ/2, and 3λ/4.

For the \(3.0\,\mathrm{kg}\) mass and 1200 N m⁻¹ spring of the preceding exercise, amplitude is \(2.0\,\mathrm{cm}\) and ω=20 rad s⁻¹. Write x(t) when t=0 is (a) the mean point moving right(b) maximum extension(c) maximum compression. Compare the motions.

A \(0.50\,\mathrm{m}\) brass rod is joined end-to-end to a \(0.50\,\mathrm{m}\) steel rod; both are free at their outer ends. Find total elongation from 40°C to 250°C for αbrass=2.0×10⁻⁵ K⁻¹ and αsteel=1.2×10⁻⁵ K⁻¹, and decide whether the junction is thermally stressed.

Initially \(10.0\,\mathrm{cm}\) of water balances \(12.5\,\mathrm{cm}\) of spirit above level mercury surfaces. Then \(15.0\,\mathrm{cm}\) of each liquid is added to its arm. Find the mercury-level difference; SGmercury=13.6.

A horizontal \(15\,\mathrm{kg}\) rigid bar hangs from three equal-length vertical wires. The two outer wires are copper and the central wire is iron. If all three tensions are equal and the bar stays level, find the copper-to-iron diameter ratio. Use Yiron=1.9×10¹¹ Pa and Ycopper=1.1×10¹¹ Pa.

For a uniform hemispherical shell, determine the gravitational field direction at the centre from the independently drawn symmetry diagram.

Equal constant torques act for equal times on a hollow cylinder and a solid sphere with the same mass and radius. Which reaches the greater angular speed?

A \(0.40\,\mathrm{kg}\) body initially moves north at \(10\,\mathrm{m\,s^{-1}}\). A constant 8.0 N force acts south from t=0 to \(30\,\mathrm{s}\). With north positive and x(0)=0, find

A driver travels \(500\,\mathrm{m}\), turns left by 60 degrees, and repeats. Find displacement and path length at the third, sixth and eighth turns.

A person walks \(2.5\,\mathrm{km}\) to a market at \(5\,\mathrm{km\,h^{-1}}\), immediately turns back at \(7.5\,\mathrm{km\,h^{-1}}\), and is home at 50 min. Find average-velocity magnitude and average speed over 0-30 min, 0-50 min and 0-40 min.