Under certain conditions, the human body can safely withstand anacceleration of 10 g.(a)

What is force? Identify several of the forces that are acting on or around you right now.

What is weight? Under what circumstances might something be weightless?

A person places a book on the roof of a car and drives off without remembering to remove it. As the book and the car move down a street at a steady speed, two horizontal forces are acting on the book. What are they?

Name the two types of friction. Can both types act on the same object at the same time? If so, give an example of such a circum- stance.

A person places a hand on a closed book resting on a table and then presses downward while pushing outward. Either the book slides across the table or the hand slides across the book. What deter- mines which event happens? Which type(s) of friction is (are) involved?

What do we mean by external force? In light of Newtons third law of motion, why cant an internal force alone produce an acceler- ation of a system?

At one moment in a football game, player A exerts a force to the east on player B. At the same time, a teammate of A exerts the same- sized force to the south on player B. In what direction is B likely to go because of these forces?

How does an object move when it is subject to a steady centripetal force? How does it move if that force suddenly disappears?

A person is riding on a train while watching the display on a GPS unit (refer back to Figure 1.9). The person notices that both the speed and the heading readings are not changing. What can the person conclude about the net force acting on the train car?

Discuss the distinction between mass and weight.

Two astronauts in an orbiting space station play catch (throw a ball back and forth to each other). Compared to playing catch on Earth, what effect, if any, does the weightless environment have on the process of accelerating (throwing and catching) the ball?

An extreme roller coaster is moving along its track. During a brief period the track exerts a downward force on the cars. Describe what is happening. (What is the shape of the track at this point?)

A single-engine airplane usually has its propeller in the front. Boats and ships usually have their propeller(s) in the rear. From the perspective of Newtons second law of motion, is this signifi- cant?

As a rocket ascends, its acceleration increases even if the net force on it stays constant. Why?

What is the international system of units (SI)?

An archer aims an arrow precisely horizontally over a large, flat field and lets it fly. At the same instant, the archers watchband breaks and the watch falls to the ground. Does the watch hit the ground before, at the same time as, or after the arrow hits the ground? Defend your answer.

Describe the variation of the net force on and the acceleration of a mass on a spring as it executes simple harmonic motion.

Explain how the change in the force of air resistance on a falling body causes it to eventually reach a terminal speed.

The terminal speed of a ping-pong ball is about 20 mph. From the top of a tall building on a windless day, a ping-pong ball is thrown downward with an initial speed of 50 mph. Describe what happens to the balls speed as it moves downward from the moment it is thrown to the moment when it hits the ground.

At least two forces are acting on you right now. What are these forces? Describe the relationship between the size and direction of these two forces.

As any car travels with constant velocity on a straight, flat section of highway, the road still exerts both a vertical (upward or downward) force and a horizontal (forward or backward) force on the car. Identify the specific direction of each of these forces.

How is Newtons third law of motion involved when you jump straight upward?

Jane and John are both on roller skates and facing each other. First Jane pushes John with her hands and they move apart. They get together again, and John pushes Jane equally hard with his hands and they move apart. Is their subsequent motion any different in the two cases? Why or why not?

What would be the gravitational force on you if you were at a point in space a distance R (Earths radius) above Earths surface?

Describe how the magnitude of the gravitational force between objects was first measured

Imagine that two identical containers, one filled with marbles and the other filled with Styrofoam beads, are released simultane- ously from rest from the same heightsay, 3 mabove Earth's surface. (a) Which container, if either, experiences the greater gravitational force? Justify your answer. (b) Which container, if either, experiences the greater acceleration from gravity? Again, justify your answer.

If suddenly the value of G, the gravitational constant, increased to a billion times its actual value, give several examples of the kinds of things that would happen. (Think locally as well as globally.)

The first Lunar Olympics is to be held on the Moon inside a huge dome. Of the usual Olympic eventstrack and field, swimming, gymnastics, and so onwhich would be drastically affected by the Moons lower gravity? In which events do you think Earth-based records would be broken? In which events would the performances be no betteror perhaps worsethan on Earth?

In the broadest terms, what causes tides?

The Suns mass is very much larger than the Moons, yet the tides on Earth produced by the Sun are much lower than those caused by the Moon. Why?

We have studied four different laws authored by Sir Isaac Newton. For each of the following, indicate which law is best for the task described. (a) Calculating the net force on a car as it slows down. (b) Calculating the force exerted on a satellite by Earth. (c) Showing the mathematical relationship between mass and weight. (d) Explaining the direction that a rubber stopper takes after the string that was keeping it moving in a circle overhead is cut. (e) Explaining why a gun recoils when it is fired. (f) Explaining why a wing on an airplane is lifted upward as it moves through the air.

What mathematical tool did Newton develop that has been essential to advanced physics ever since?

Express your weight in newtons. From this determine your mass in kilograms.

A child weighs 300 N. What is the childs mass?

Suppose an airline allows a maximum of 30 kg for each suitcase a passenger brings along. (a) What is the weight in newtons of a 30-kg suitcase? (b) What is the weight in pounds?

The mass of a certain elephant is 1,130 kg. (a) Find the elephants weight in newtons. (b) Find its weight in pounds.

The mass of a subway car and passengers is 40,000 kg. If its accel- eration as it leaves a station is 0.9 m/s2 , what is the net force acting on it?

A motorcycle and rider have a total mass equal to 300 kg. The rider applies the brakes, causing the motorcycle to accelerate at a rate of 5 m/s2 . What is the net force on the motorcycle?

As a 2-kg ball rolls down a ramp, the net force on it is 10 N. What is the acceleration?

In an experiment performed in a space station, a force of 60 N causes an object to have an acceleration equal to 4 m/s2 . What is the objects mass?

The engines in a supertanker carrying crude oil produce a net force of 20,000,000 N on the ship. If the resulting acceleration is 0.1 m/s2 , what is the ships mass?

The Kingda Ka roller coaster in New Jersey is the worlds tallest ride of its kind. As the passenger cars are launched from rest at the start, they are accelerated uniformly to a speed of 57 m/s (128 mph) in just 3.5 s. (a) What is the acceleration experienced by passengers on this ride in m/s2 ? In gs? (b) If a certain passenger has a mass of 65 kg, what is the force that acts on him during the launch phase of this ride in newtons? In pounds?

A person stands on a scale inside an elevator at rest ( Figure 2.51). The scale reads 800 N. (a) What is the persons mass? (b) The elevator accelerates upward momentarily at the rate of 2 m/s2 . What does the scale read then? (c) The elevator then moves with a steady speed of 5 m/s. What does the scale read now?

A jet aircraft with a mass of 4,500 kg has an engine that exerts a force (thrust) equal to 60,000 N. (a) What is the jets acceleration when it takes off?(b) What is the jets speed after it accelerates for 8 s? (c) How far does the jet travel during the 8 s?

At the end of Section 1.4, we mentioned that the maximum acceler- ation of a fist during a particular karate blow was measured to be about 3,500 m/s2 (Figure 1.30). (a) If the mass of the fist was approximately 0.7 kg, what was the maximum force? (b) What was the maximum force on the concrete block?

A sprinter with a mass of 80 kg accelerates from 0 m/s to 9 m/s in 3 s. (a) What is the runners acceleration? (b) What is the net force on the runner? (c) How far does the sprinter go during the 3 s?

As a baseball is being caught, its speed goes from 30 to 0 m/s in about 0.005 s. Its mass is 0.145 kg. (a) What is the baseballs acceleration in m/s2 and in gs? (b) What is the size of the force acting on it?

On aircraft carriers, catapults are used to accelerate jet aircraft to flight speeds in a short distance. One such catapult takes a 18,000-kg jet from 0 to 70 m/s in 2.5 s. (a) What is the acceleration of the jet (in m/s2 and gs)? (b) How far does the jet travel while it is accelerating? (c) How large is the force that the catapult must exert on the jet?

At the end of an amusement park ride, it is desirable to bring a gon- dola to a stop without having the acceleration exceed 2 g. If the total mass of the gondola and its occupants is 2,000 kg, what is the maxi- mum allowed braking force?

An airplane is built to withstand a maximum acceleration of 6 g. If its mass is 1,200 kg, what size force would cause this acceleration?

Under certain conditions, the human body can safely withstand an acceleration of 10 g. (a) What net force would have to act on someone with mass of 50 kg to cause this acceleration? (b) Find the weight of such a person in pounds, then convert the answer to (a) to pounds.

A race car rounds a curve at 60 m/s. The radius of the curve is 400 m, and the cars mass is 600 kg. (a) What is the cars (centripetal) acceleration? What is it in gs? (b) What is the centripetal force acting on the car?

A hang glider and its pilot have a total mass equal to 120 kg. While executing a 360 turn, the glider moves in a circle with an 8-m radius. The gliders speed is 10 m/s. (a) What is the net force on the hang glider? (b) What is the acceleration?

A 0.1-kg ball is attached to a string and whirled around in a circle overhead. The string breaks if the force on it exceeds 60 N. What is the maximum speed the ball can have when the radius of the circle is 1 m?

On a highway curve with radius 50 m, the maximum force of static friction (centripetal force) that can act on a 1,000-kg car going around the curve is 8,000 N. What speed limit should be posted for the curve so that cars can negotiate it safely?

A centripetal force of 200 N acts on a 1,000-kg satellite moving with a speed of 5,000 m/s in a circular orbit around a planet. What is the radius of its orbit?

As a spacecraft approaches a planet, the rocket engines on it are fired (turned on) to slow it down so it will go into orbit around the planet. The spacecrafts mass is 2,000 kg, and the thrust (force) of the rocket engines is 400 N. If its speed must be decreased by 1,000 m/s, how long must the engines be fired? (Ignore the change in the mass as the fuel is burned.)

A space probe is launched from Earth headed for deep space. At a distance of 10,000 miles from Earths center, the gravitational force on it is 600 lb. What is the size of the force when it is at each of the following distances from Earths center? (a) 20,000 miles (b) 30,000 miles (c) 100,000 miles

The force on a baseball as it is being hit with a bat can be more than 8,000 lb. No human can push on a bat with that much force. What is happening in this instance?

Two forces, one equal to 15 N and another equal to 40 N, act on a 50-kg crate resting on a horizontal surface as shown in the accompa- nying figure. (a) What is the net horizontal force on the crate? (b) What is its horizontal acceleration? (c) If the crate starts from rest, what is its horizontal speed after 5 s? (d) How far has the crate traveled along the surface in this time?

Why does banking a curve on a highway allow a vehicle to success- fully negotiate the turn at a higher speed?

4. As a horse and wagon are accelerating from rest, the horse exerts a force of 400 N on the wagon ( Figure 2.53). Illustrating Newtons third law, the wagon exerts an equal and opposite force of 400 N. Because the two forces are in opposite directions, why dont they cancel each other and produce zero acceleration (i.e., no motion)?

Perform the calculation of the force acting between two 70-kg peo- ple standing 1 m apart to verify the result given on p. 72.

Perhaps youve noticed that the rockets used to put satellites and spacecraft into orbit are usually launched from pads near the equa- tor. Why is this so? Is the fact that rockets are usually launched to the east also important? Why?

7. The acceleration of a freely falling body is not exactly the same everywhere on Earth. For example, in the Galapagos Islands at the equator, the acceleration of a freely falling body is 9.780 m/s2 , whereas at the latitude of Oslo, Norway, it is 9.831 m/s2 . Why does the acceleration differ?

A 200-kg communications satellite is placed into a circular orbit around Earth with a radius of 4.23 107 m (26,300 miles) (see Figure 2.54). (a) Find the gravitational force on the satellite. (There is some useful information in Section 2.8.) (b) Use the equation for centripetal force to compute the speed of the satellite. (c) Show that the period of the satellitethe time it takes to com- plete one orbitis 1 day. (The distance it travels during one orbit is 2p, or 6.28, times the radius.) This is a geosynchronous orbit: the satellite stays above a fixed point on Earths equator.

Complete the calculation of the mass of Earth as outlined in Section 2.8.

During our discussion of the motion of a falling body, we said that the gravitational force acting on itits weightis constant. But the law of universal gravitation tells us that the gravitational force on a body increases as it gets closer to Earths center. Is there a contradic- tion here? Explain. (Hint: Calculate the gravitational force an a 1-kg mass located on Earths surface and then repeat the calculation for the same mass located 10 m above Earths surface. Compare your answers.)