On July 10,1996, a granite block broke away from a wall in...

On July $10,1996,$ a granite block broke away from a wall in Yosemite Valley and, as it began to slide down the wall, was launched into projectile motion. Seismic waves produced by its impact with the ground triggered seismographs as far away as 200 $\mathrm{km} .$ Later measurements indicated that the block had a mass between $7.3 \times 10^{7} \mathrm{kg}$ and $1.7 \times 10^{8} \mathrm{kg}$ and that it landed 500 $\mathrm{m}$ vertically below the launch point and 30 $\mathrm{m}$ horizontally from it. (The launch angle is not known.) (a) Estimate the block's kinetic energy just before it landed. Consider two types of seismic waves that spread from the impact point $-a$ hemispherical body wave traveled through the ground in an expanding hemisphere and a cylindrical surface wave traveled along the ground in an expanding shallow vertical cylin- der (Fig. $17-49 )$ . Assume that the impact lasted 0.50 s, the vertical cylinder had a depth $d$ of $5.0 \mathrm{m},$ and each wave type received 20$\%$ of the energy the block had just before impact. Neglecting any mechanical energy loss the waves experienced as they traveled, determine the intensities of (b) the body wave and (c) the surface wave when they reached a seismograph 200 $\mathrm{km}$ away. (d) On the basis of these results, which wave is more easily detected on a distant seismograph?

On July $10,1996,$ a granite block broke away from a wall in Yosemite Valley and, as it began to slide down the wall, was
launched into projectile motion. Seismic waves produced by its
impact with the ground triggered seismographs as far away as 200 $\mathrm{km} .$ Later measurements indicated that the block had a mass
between $7.3 \times 10^{7} \mathrm{kg}$ and $1.7 \times 10^{8} \mathrm{kg}$ and that it landed 500 $\mathrm{m}$
vertically below the launch point and 30 $\mathrm{m}$ horizontally from it. (The launch angle is not known.) (a) Estimate the block's kinetic
energy just before it landed.
Consider two types of seismic waves that spread from the impact point $-a$ hemispherical body wave traveled through the
ground in an expanding hemisphere and a cylindrical surface wave traveled along the ground in an expanding shallow vertical cylin-
der (Fig. $17-49 )$ . Assume that the impact lasted 0.50 s, the vertical
cylinder had a depth $d$ of $5.0 \mathrm{m},$ and each wave type received 20$\%$
of the energy the block had just before impact. Neglecting any mechanical energy loss the waves experienced as they traveled,
determine the intensities of (b) the body wave and (c) the surface
wave when they reached a seismograph 200 $\mathrm{km}$ away. (d) On the
basis of these results, which wave is more easily detected on a
distant seismograph?

Key Concepts

Seismic Wave Propagation

Seismic wave propagation pertains to the way energy from an impact distributes through the Earth in the form of waves. This typically involves body waves, which travel through the medium (often spreading out hemispherically), and surface waves, which are constrained to the near-surface region (spreading cylindrically). Understanding the different geometries of wave propagation is key in assessing how energy distribution decreases with distance.

Intensity and Energy Distribution

Intensity in the context of wave phenomena is defined as the energy per unit area per unit time. Calculating the intensities of seismic waves involves dividing the energy that enters each wave by the area over which the energy is spread as the wave propagates. This concept is essential for understanding how energy amplitudes diminish with distance and why certain types of waves may be more easily detected at large distances.

Kinetic Energy

Kinetic energy is a measure of an object’s energy due to its motion, typically calculated using the formula (1/2)mv². In problems involving impacting objects, estimating the kinetic energy at the moment of impact provides crucial information about the energy available for conversion into other forms, such as seismic energy in an impact event.

Projectile Motion and Energy Conservation

Projectile motion involves the movement of an object under the influence of gravity, where its initial potential energy is converted to kinetic energy as it descends. Energy conservation principles allow us to relate the changes in gravitational potential energy to the kinetic energy just before impact, even when the launch angle is unknown.