The gravitational field strength at Earth’s surface is 9.8 N/kg. What is the field strength at the center of Earth? At a distance one Earth radius beyond the surface?

The mass of Earth is about 80 times that of the moon and its radius is about 3.7 times that of the moon. Calculate the acceleration due to gravity at the surface of the moon. Express your answer in g’s

A true–false quiz has ten questions. A student guesses all the answers. (a) Find the probability of getting eight correct. (b) Find the probability of getting at least eight correct. (c) Find the probability of getting no more than two correct.

Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 360 km above the earth's surface, while that for satellite B is at a height of 720 km. Find the orbital speed for each satellite.

Why are tides greater at the times of the full and new moons and at the times of lunar and solar eclipses?

Refer to the partially completed table below of the 10 basic solutions to the e-system

$$\begin{aligned} x_{1}+x_{2}+s_{1} &=24 \\ 2 x_{1}+x_{2} &+s_{2}=30 \\ 4 x_{1}+x_{2} &+s_{3}=48 \end{aligned}$$

$$\begin{matrix} \text{} & \text{}{x_{1}} & \text{}{x_{2}} & \text{}{s_{1}} & \text{}{s_{2}} & \text{}{s_{3}}\\ \text{(A)} & \text{0} & \text{0} & \text{24} & \text{30} & \text{48}\\ \text{(B)} & \text{0} & \text{24} & \text{0} & \text{6} & \text{24}\\ \text{(C)} & \text{0} & \text{30} & \text{-6} & \text{0} & \text{18}\\ \text{(D)} & \text{0} & \text{48} & \text{-24} & \text{-18} & \text{0}\\ \text{(E)} & \text{24} & \text{0} & \text{0} & \text{-18} & \text{-48}\\ \text{(F)} & \text{15} & \text{0} & \text{9} & \text{0} & \text{-12}\\ \text{(G)} & \text{} & \text{0} & \text{} & \text{} & \text{0}\\ \text{(H)} & \text{} & \text{} & \text{0} & \text{0} & \text{}\\ \text{(I)} & \text{} & \text{} & \text{0} & \text{} & \text{0}\\ \text{(J)} & \text{} & \text{} & \text{} & \text{0} & \text{0}\\ \end{matrix}$$

In basic solution (E), which variables are nonbasic?

A compound containing only C, H, and N yields the following data. i. Complete combustion of 35.0 mg of the compound produced 33.5 mg of $\mathrm { CO } _ { 2 }$ and 41.1$\ \mathrm { mg }$ of $\mathrm { H } _ { 2 } \mathrm { O }$. ii. A 65.2-g sample of the compound was analyzed for nitrogen by the Dumas method, giving 35.6$\ \mathrm { mL }$ of dry $\mathrm { N } _ { 2 }$ at $740 .$ torr and $25 ^ { \circ } \mathrm { C }.$ iii. The effusion rate of the compound as a gas was measured and found to be 24.6 mL/min. The effusion rate of argon gas, under identical conditions, is 26.4 mL/min. What is the formula of the compound?

A kilogram of water on the side of Earth nearest the moon is gravitationally attracted to the moon with a greater force than a kilogram of water on the side of Earth farthest from the moon. The difference in force per mass, the tidal force, is approximated by

$$F _ { \mathrm { T } } = \frac { 4 G M R } { d ^ { 3 } }$$

where G is the gravitational constant, M is the mass of the moon, R is the radius of Earth, and d is the distance between the centers of the moon and Earth. Calculate

$$F_T$$

of the moon on Earth in units

$$\mathrm { N } / \mathrm { kg } . ( M = 7.35 \times 10 ^ { 22 } \mathrm { kg } , R = 6.4 \times 10 ^ { 6 } \mathrm { m }, \text {and} d = 3.85 \times 10 ^ { 8 } \mathrm { m } )$$

A popular amusement park ride for young children is the carousel or merry-go-round. A typical carousel consists of a circular platform with three circles of horses to ride, an inner circle, a middle circle, and an outer circle. Children and sometimes adults ride these horses as the carousel goes round and round. In which circle should a child ride for the slowest-ride? For the fastest ride? Why?

A ride at an amusement park consists of two circular rings of swings. At full speed, the swings in the inner ring travel on a circular path with a radius of $32$ feet, and the swings in the outer ring travel on a circular path with a radius of $38$ feet. Each swing makes one complete revolution every $3.75$ seconds. How much greater, in miles per hour, is the linear speed of the swings in the outer ring than the linear speed of the swings in the inner ring? Round to the nearest tenth.

Solve each triangle. $a=2,\ b=2,\ C=50^{\circ}$

A kilogram of water on the side of Earth nearest the moon is gravitationally attracted to the moon with a greater force than a kilogram of water on the side of Earth farthest from the moon. The difference in force per mass, the tidal force, is approximated by

$$F _ { \mathrm { T } } = \frac { 4 G M R } { d ^ { 3 } }$$

where G is the gravitational constant, M is the mass of the moon, R is the radius of Earth, and d is the distance between the centers of the moon and Earth. If you stand on Earth directly under the moon, the moon’s tidal pull will slightly stretch you, pulling harder on your head than on your feet. Your head and feet are not part apart like Earth’s oceans are, so R in the tidal force equation is only about half your height rather than half Earth’s diameter. Approximately the

$$F_T$$

of the moon on you.

Friction provides the force needed for a car to travel around a flat, circular race track. What is the maximum speed at which a car can safely travel if the radius of the track is 80.0 m and the coefficient of friction is 0.40?

A proton is suspended in the air by an electric field at the surface of Earth. What is the strength of this electric field?