Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a “crumple zone” in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about $1m$as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton’s first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about $5mm$. a. A $60kg$ person is in a head-on collision. The car’s speed at impact is $15m/s$. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.

b. Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag

Sam, whose mass is $75$ kg, takes off across level snow on his jet-powered skis. The skis have a thrust of $200$ N and a coefficient of kinetic friction on snow of $0.10$. Unfortunately, the skis run out of fuel after only$10$ s.

a. What is Sam’s top speed?

b. How far has Sam traveled when he finally coasts to a stop?

An elevator, hanging from a single cable, moves downward and is slowing. Friction and air resistance are negligible. Is the tension in the cable greater than, less than, or equal to the gravitational force on the elevator? Explain. Include a free-body diagram as part of your explanation.

The four balls in FIGURE Q6.9 have been thrown straight up. They have the same size, but different masses. Air resistance is negligible. Rank in order, from largest to smallest, the magnitude of the net force acting on each ball. Some may be equal. Give your answer in the form $a>b>c=d$ and explain your ranking.

Astronauts in space "weigh" themselves by oscillating on a CALC spring. Suppose the position of an oscillating $75\mathrm{kg}$ astronaut is given by$x=\left(0.30\mathrm{m}\right)\sin \left(\right(\pi \mathrm{rad}/\mathrm{s})\times t)$, where $t$ is in $\mathrm{s}$. What force does the spring exert on the astronaut at

(a) $t=1.0\mathrm{s}$ and

(b) $1.5\mathrm{s}$ ? Note that the angle of the sine function is in radians.

A hand presses down on the book in FIGURE Q6.12. Is the normal force of the table on the book larger than, smaller than, or equal to mg?