An unbalanced baton consists of a 50-cm-long uniform rod of mass $200 \mathrm{~g}$. At one end there is a 10 -cm-diameter uniform solid sphere of mass $500 \mathrm{~g}$, and at the other end there is a $8.0-\mathrm{cm}-$ diameter uniform solid sphere of mass $750 \mathrm{~g}$. (The center-to-center distance between the spheres is $59 \mathrm{~cm}$.)

$(b)$ If this baton is tossed straight up (but spinning) so that its initial center of mass speed is $10.0 \mathrm{~m} / \mathrm{s}$, what is the velocity of the center of mass $1.5 \mathrm{~s}$ later?

In a carnival ride, you sit on a seat in a compartment that rotates with constant speed in a vertical circle of radius $5.0 \mathrm{~m}$. The ride is designed so your head always points toward the center of the circle.

$(a)$ If the ride completes one full circle in $2.0 \mathrm{~s}$, find the direction and magnitude of your acceleration.

The speed of the head of a red headed woodpecker reaches $5.5 \mathrm{~m} / \mathrm{s}$ before impact with the tree. If the mass of the head is $0.060 \mathrm{~kg}$ and the average force on the head is $6.0 \mathrm{~N}$, find

$(b)$ the depth of penetration into the tree.

A redheaded woodpecker hits the bark of a tree extremely hard-the speed of its head reaches approximately $v=3.5 \mathrm{~m} / \mathrm{s}$ before impact. If the mass of the bird's head is $0.060 \mathrm{~kg}$, and the average force acting on the head during impact is $F=6.0 \mathrm{~N}$, find ( $($ ) the acceleration of its head (assuming it is constant), $(b)$ the depth of penetration into the bark, and (c) the time $t$ it takes the woodpecker's head to stop.

The bottom end of a massless, vertical spring of force constant $k$ rests on a scale and the top end is attached to a massless cup, as in Figure 5-81. Place a ball of mass $m_{\mathrm{b}}$ gently into the cup and ease it down into an equilibrium position where it sits at rest in the cup.

$(b)$ Show that in this situation, the spring compression $d$ is given by $d=m_{\mathrm{b}} g / k$.

The La Quebrada Cliff Divers perform shows for the public by jumping into the sea off the cliffs at Acapulco, Mexico. The height (in feet) of a diver at a certain time (in seconds) is given by $h = - 16 t ^ { 2 } + 16 t + 400$ a. Use the vertex and y-intercept to make a sketch that represents the dive. What form of the quadratic function helps you determine they-intercept efficiently? What form helps you determine the vertex easily? b. At what height did the diver start his jump? What is the maximum height he achieved?

An unbalanced baton consists of a 50-cm-long uniform rod of mass $200 \mathrm{~g}$. At one end there is a 10 -cm-diameter uniform solid sphere of mass $500 \mathrm{~g}$, and at the other end there is a $8.0-\mathrm{cm}-$ diameter uniform solid sphere of mass $750 \mathrm{~g}$. (The center-to-center distance between the spheres is $59 \mathrm{~cm}$.)

$(a)$ Where, relative to the center of the light sphere, is the center of mass of this baton?

A circular plate of radius $R$ has a circular hole of radius $R / 2$ cut out of it (Figure 5-86). Find the center of mass of the plate after the hole has been cut. Hint: The plate can be modeled as two disks superimposed, with the hole modeled as a disk negative mass.

Find the location of the center of mass of the Earth-moon system relative to the center of Earth. Is it inside or outside the surface of Earth?

A child of mass $m$ slides down a slide inclined at $30^{\circ}$ in time $t_1$. The coefficient of kinetic friction between her and the slide is $\mu_{\mathrm{k}}$. She finds that if she sits on a small sled (also of mass $m$ ) with frictionless runners, she slides down the same slide in time $\frac{1}{2} t_1$. Find $\mu_{\mathrm{k}}$.

After a parachutist jumps from an airplane (but before he pulls the rip cord to open his parachute), a downward speed of up to $180 \mathrm{~km} / \mathrm{h}$ can be reached. When the parachute is finally opened, the drag force is increased by about a factor of 10, and this can create a large jolt on the jumper. Suppose this jumper falls at $180 \mathrm{~km} / \mathrm{h}$ before opening his chute.

$(b)$ If rapid accelerations greater than $5.0 \mathrm{~g}$ can harm the structure of the human body, is this a safe practice?

After a parachutist jumps from an airplane (but before he pulls the rip cord to open his parachute), a downward speed of up to $180 \mathrm{~km} / \mathrm{h}$ can be reached. When the parachute is finally opened, the drag force is increased by about a factor of 10, and this can create a large jolt on the jumper. Suppose this jumper falls at $180 \mathrm{~km} / \mathrm{h}$ before opening his chute.

$(a)$ Determine the parachutist's acceleration when the chute is just opened, assuming his mass is $60 \mathrm{~kg}$.

Sally claims flying squirrels do not really fly; they jump and use the folds of skin that connect their forelegs and their back legs like a parachute to allow them to glide from tree to tree. Liz decides to test Sally’s hypothesis by calculating the terminal speed of a falling outstretched flying squirrel. If the constant b in the drag force is proportional to the area of the object facing the air flow, use the results of Example 5-12 and some assumptions about the size of the squirrel to estimate its terminal (downward) speed. Is Sally’s claim supported by Liz’s calculation?

An block of mass $m_1$ is on a horizontal table. The block is attached to a $2.5-\mathrm{kg}$ block $\left(m_2\right)$ by a light string that passes over a pulley at the edge of the table. The block of mass $m_2$ dangles $1.5 \mathrm{~m}$ above the ground (Figure 5-85). The string that connects them passes over a frictionless, massless pulley. This system is released from rest at $t=0$ and the $2.5-\mathrm{kg}$ block strikes the ground at $t=0.82 \mathrm{~s}$. The system is now placed in its initial configuration and a $1.2-\mathrm{kg}$ block is placed on top of the block of mass $m_1$. Released from rest, the $2.5-\mathrm{kg}$ block now strikes the ground $1.3 \mathrm{~s}$ later. Determine the mass $m_1$ and the coefficient of kinetic friction between the block whose mass is $m_1$ and the table.