Chapter 1: Mechanics

While driving in an exotic foreign land, you see a speed limit sign that reads 180,000 furlongs per fortnight. How many miles per hour is this? (One furlong is 1/8 mile, and a fortnight is 14 days. A furlong originally referred to the length of a plowed furrow.)

A 1130-kg car is held in place by a light cable on a very smooth (frictionless) ramp (Fig. E5.8). The cable makes an angle of 31.0° above the surface of the ramp, and the ramp itself rises at 25.0° above the horizontal.

(a) Draw a free-body diagram for the car.

(b) Find the tension in the cable.

(c) How hard does the surface of the ramp push on the car?

Black smokers are hot volcanic vents that emit smoke deep in the ocean floor. Many of them teem with exotic creatures, and some biologists think that life on earth may have begun around such vents. The vents range in depth from about 1500 m to 3200 m below the surface. What is the gauge pressure at a 3200-m deep vent, assuming that the density of water does not vary? Express your answer in Pascal and atmospheres.

An $\mathbf{8}.\mathbf{00}\mathbf{kg}$ point mass and a$\mathbf{12}.\mathbf{00}\mathbf{kg}$ point mass are held$\mathbf{50}.\mathbf{0}\mathbf{cm}$ apart. A particle of mass mis released from a point between the two masses$\mathbf{20}.\mathbf{0}\mathbf{cm}$ from the$\mathbf{8}.\mathbf{00}-\mathbf{kg}$ group along the line connecting the two fixed masses. Find the magnitude and direction of the acceleration of the particle.

BIO Bone Fractures.The maximum energy that a bone canabsorb without breaking depends on characteristics such as its $\mathbf{6}\mathbf{.}\mathbf{0}\mathit{c}{\mathit{m}}^{\mathbf{2}}$cross-sectional area and elasticity. For healthy human leg bones of approximately cross-sectional area, this energy has been experimentally measured to be about $\mathbf{200}\mathit{J}$. (a) From approximately what maximum height could a $\mathbf{\text{60 kg}}$ person jump and landrigidly upright on both feet without breaking his legs? (b) You areprobably surprised at how small the answer to part (a) is. People obviously jump from much greater heights without breaking their legs. How can that be? What else absorbs the energy when they jump from greater heights? (Hint: How did the person in part (a)land? How do people normally land when they jump from greater heights?) (c) Why might older people be much more prone than younger ones to bone fractures from simple falls (such as a fall in the shower)?

A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force $\overrightarrow{\mathbf{F}}\mathbf{=}\left(30N\right)\hat{\mathbf{i}}\mathbf{‐}\left(40N\right)\hat{\mathbf{j}}$to the cart as it undergoes a displacement $\overrightarrow{\mathbf{s}}\mathbf{=}\left(‐9.0m\right)\hat{\mathbf{i}}\mathbf{‐}\left(3.0m\right)\hat{\mathbf{j}}$. How much work does the force you apply do on the grocery cart?

A uniform disk with mass 40.0 kg and radius 0.200 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force is applied tangent to the rim of the disk. (a) What is the magnitude $\mathit{\nu }$of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.200 revolution? (b) What is the magnitude aof the resultant acceleration of a point on the rim of the disk after the disk has turned through 0.200 revolution?

The maximum energy that a bone can absorb without breaking depends on characteristics such as its cross-sectional area and elasticity. For healthy human leg bones of approximately $\mathbf{6}\mathbf{.}\mathbf{0}{\mathbf{\text{cm}}}^{\mathbf{\text{2}}}$cross-sectional area, this energy has been experimentally measured to be about $\mathbf{200}\mathbf{\text{J}}$. (a) From approximately what maximum height could a $\mathbf{\text{60 kg}}$ person jump and land rigidly upright on both feet without breaking his legs? (b) You are probably surprised at how small the answer to part (a) is. People obviously jump from much greater heights without breaking their legs. How can that be? What else absorbs the energy when they jump from greater heights? (Hint: How did the person in part (a) land? How do people normally land when they jump from greater heights?) (c) Why might older people be much more prone than younger ones to bone fractures from simple falls (such as a fall in the shower)?

Force of a Baseball Swing. A baseball has mass 0.145 kg.

(a) If the velocity of a pitched ball has a magnitude of

and the batted ball’s velocity is in the opposite direction,

find the magnitude of the change in momentum of the ball and

of the impulse applied to it by the bat. (b) If the ball remains in

contact with the bat for 2.00 ms, find the magnitude of the average

force applied by the bat.

$\mathbf{}\mathbf{A}\mathbf{}\mathbf{60}\mathbf{.}\mathbf{0}\mathbf{-}\mathbf{m}$uniform $\mathbf{50}\mathbf{.}\mathbf{0}\mathbf{-}\mathbf{N}$, shelf is supported horizontally by two vertical wires attached to the sloping ceiling (Fig. E11.8). A very small $\mathbf{25}\mathbf{.}\mathbf{0}\mathbf{-}\mathbf{N}$tool is placed on the shelf midway between the points where the wires are attached to it. Find the tension in each wire. Beginby making a free-body diagram of the shelf.