The world's largest ball of twine was made by one man in Minnesota in the United States. A basketball sitting $55.0 \mathrm{~m}$ (measured from centre to centre) from the ball of twine would experience a gravitational field of $1.74 \times 10^{-10} \mathrm{~N} / \mathrm{kg}$ from the ball of twine. Calculate the ball of twine's mass.

An airplane flying due north has an air speed of 500 m/h. There is a northwesterly wind of 60 km/h. Find the true speed and direction of the plane relative to the ground.

At the end of a delivery ramp, a skid pad exerts a constant force on a package so that the package comes to rest in a distance d. When the pad is replaced by one that requires a distance of 2d to stop the same package, what happens to the length of time it takes for the package to stop?

An archer needs to hit a bull's eye on a target at eye level $60.0 \mathrm{ft}$ away. Will the arrow hit the target, If the archer fires the arrow from eye level with a speed of $47.0 \mathrm{ft} / \mathrm{s}$ at an angle of $25.0^{\circ}$ above the horizontal?

The potential energy of an interaction is given by $U ( x ) = a x ^ { 2 }$, where $a = + 6.4 \mathrm { J } / \mathrm { m } ^ { 2 }$. (a) If the initial speed of a 0.82-kg object in this system is 2.23 m/s at x = 0, how far does the object travel before it reaches a speed of v = 0? (b) Does your answer in part a depend on whether the object is traveling in the positive or negative x direction?

A 0.70-kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstrained length triples. What is the mass of the second block?

Calculate the strength of the gravitational field of a $6520 \mathrm{~kg}$ elephant at a distance of $5.75 \mathrm{~m}$.

The circuit shown in Figure is a second-order low-pass filter. This filter circuit is called a multiple-loop feedback filter (MFF). The output impedance of this filter is zero, so the MFF low-pass filter is suitable for use as a filter stage in a cascade filter. The transfer function of the low-pass MFF filter is Design this filter to have $\omega_0=2000 \mathrm{rad} / \mathrm{s}$ and $Q=8$. What is the value of the dc gain?

Henry Cavendish used freely moving balls to measure the gravitational force between two masses on Earth's surface. Suppose a scientist repeated the measurement using masses $m_1=0.032 \mathrm{~kg}$ and $m_2=5500 \mathrm{~kg}$. What is the gravitational force between the masses when the distance between their centres is $r=0.75 \mathrm{~m}$ ?

Explain why black holes are so difficult for scientists to study.

Ball A, with mass $m$, is a distance $d$ from ball B, which has a mass of $3 \mathrm{~m}$. At which of the following distances is the gravitational attraction of the balls on each other equal? (a) $\frac{d}{9}$ (b) $\frac{d}{3}$ (c) $\frac{2 d}{3}$ (d) any separation distance

Suppose a planet has half the mass of Earth but the same radius. An astronaut stands on the surface of the planet and drops a rock from a height of $2.4 \mathrm{~m}$. How much longer does it take the rock to hit the ground on that planet than it would on Earth? (a) $1.2$ times longer (b) $\sqrt{2}$ times longer (c) 2 times longer (d) $4.8$ times longer

Two objects are a distance $r$ apart. The distance $r$ increases by a factor of 4 . (a) Does the gravitational force between the objects increase or decrease? Explain your answer. (b) By what factor does the gravitational force between the objects change?

Two small balls of mass $22 \mathrm{~kg}$ and $25 \mathrm{~kg}$ are a distance of $1.2 \mathrm{~m}$ apart. (a) Calculate the gravitational force between the balls. (b) How far apart would two balls of mass $16 \mathrm{~kg}$ and $21 \mathrm{~kg}$ have to be to have this same gravitational force between them?