A mass M hangs from a uniform rope of length L and mass m. Find an expression for the

Distinguish the Aristotelian and Galilean/Newtonian views of the natural state of motion.

A ball bounces off a wall with the same speed it had before it hit the wall. Has its momentum changed? Has a force acted on the ball? Has a force acted on the wall? Relate your answers to Newtons laws of motion.

We often use the term inertia to describe human sluggishness. How is this usage related to the meaning of inertia in physics?

Does a body necessarily move in the direction of the net force acting on it?

A truck crashes into a stalled car. A student trying to explain the physics of this event claims that no forces are involved; the car was just in the way so it got hit. Comment.

A barefoot astronaut kicks a ball, hard, across a space station. Does the balls apparent weightlessness mean the astronauts toes dont hurt? Explain.

The surface gravity on Jupiters moon Io is one-fifth that on Earth. What would happen to your weight and to your mass if you were on Io?

In paddling a canoe, you push water backward with your paddle. What force actually propels the canoe forward?

Is it possible for a nonzero net force to act on an object without the objects speed changing? Explain.

As your plane accelerates down the runway, you take your keys from your pocket and suspend them by a thread. Do they hang vertically? Explain.

A driver tells passengers to buckle their seatbelts, invoking the law of inertia. Whats that got to do with seatbelts?

A subway trains mass is What force is required to accelerate the train at

A 61-Mg railroad locomotive can exert a 0.12-MN force. At what rate can it accelerate (a) by itself and (b) when pulling a 1.4-Gg train?

A small plane accelerates down the runway at If its propeller provides an 11-kN force, whats the planes mass?

A car leaves the road traveling at 110 km/h and hits a tree, coming to a stop in 0.14 s. What average force does a seatbelt exert on a 60-kg passenger during this collision?

By how much does the force required to stop a car increase if the initial speed is doubled while the stopping distance remains the same?

Kinesin is a motor protein responsible for moving materials within living cells. If it exerts a 6.0-pN force, what acceleration will it give a molecular complex with mass

Starting from rest, a 940-kg racing car covers 400 m in 4.95 s. Find the average force on the car.

In an egg-dropping contest, a student encases an 85-g egg in a Styrofoam block. If the force on the egg cant exceed 1.5 N, and if the block hits the ground at 1.2 m/s, by how much must the Styrofoam compress on impact?

In a front-end collision, a 1300-kg car with shock-absorbing bumpers can withstand a maximum force of 65 kN before damage occurs. If the maximum speed for a nondamaging collision is 10 km/h, by how much must the bumper be able to move relative to the car?

Show that the units of acceleration can be written as N/kg. Why does it make sense to give g as 9.8 N/kg when talking about mass and weight?

Your spaceship crashes on one of the Suns planets. Fortunately, the ships scales are intact and show that your weight is 532 N. If your mass is 60 kg, where are you? (Hint: Consult Appendix E.)

Your friend can barely lift a 35-kg concrete block on Earth. How massive a block could she lift on the Moon?

A cereal box says net weight 340 grams. Whats the actual weight (a) in SI units and (b) in ounces?

Youre a safety engineer for a bridge spanning the U.S.-Canadian border. U.S. specifications permit a maximum load of 10 tons. What load limit should you specify on the Canadian side, where weight is given in kilograms?

The gravitational acceleration at the International Space Stations altitude is about 89% of its surface value. Whats the weight of a 68-kg astronaut at this altitude?

A 50-kg parachutist descends at a steady 40 km/h. What force does air exert on the parachute?

A 930-kg motorboat accelerates away from a dock at Its propeller provides a 3.9-kN thrust force. What drag force does the water exert on the boat?

An elevator accelerates downward at What force does the elevators floor exert on a 52-kg passenger?

At 560 metric tons, the Airbus A-380 is the worlds largest airliner. Whats the upward force on an A-380 when the plane is (a) flying at constant altitude and (b) accelerating upward at

Youre an engineer working on Ares I, NASAs replacement for the space shuttles. Performance specs call for a first-stage rocket capable of accelerating a total mass of 630 Mg vertically from rest to 7200 km/h in 2.0 min. Youre asked to determine the required engine thrust (force) and the force exerted on a 75-kg astronaut during liftoff. What do you report?

You step into an elevator, and it accelerates to a downward speed of 9.2 m/s in 2.1 s. How does your apparent weight during this time compare with your actual weight?

What upward gravitational force does a 5600-kg elephant exert on Earth?

Your friends mass is 65 kg. If she jumps off a 120-cm-high table, how far does Earth move toward her as she falls?

What force is necessary to stretch a spring 48 cm, if its spring constant is 270 N/m?

A 35-N force is applied to a spring with spring constant How much does the spring stretch?

A spring with spring constant is used to weigh a 6.7-kg fish. How far does the spring stretch?

A 1.25-kg object is moving in the x-direction at 17.4 m/s. Just 3.41 s later, its moving at 26.8 m/s at to the x-axis. Find the magnitude and direction of the force applied during this time.

An airplane encounters sudden turbulence, and you feel momentarily lighter. If your apparent weight seems to be about 70% of your normal weight, what are the magnitude and direction of the planes acceleration?

A 74-kg tree surgeon rides a cherry picker lift to reach the upper branches of a tree. What force does the lift exert on the surgeon when its (a) at rest; (b) moving upward at a steady 2.4 m/s; (c) moving downward at a steady 2.4 m/s; (d) accelerating upward at (e) accelerating downward at

A dancer executes a vertical jump during which the floor pushes up on his feet with a force 50% greater than his weight. Whats his upward acceleration?

Find expressions for the force needed to bring an object of mass m from rest to speed (a) in time and (b) over distance

An elevator moves upward at Whats its minimum stopping time if the passengers are to remain on the floor?

A 2.50-kg object is moving along the x-axis at 1.60 m/s. As it passes the origin, two forces and are applied, both in the y-direction (plus or minus). The forces are applied for 3.00 s, after which the object is at If , whats ?

Blocks of 1.0, 2.0, and 3.0 kg are lined up on a frictionless table, as shown in Fig. 4.21, with a 12-N force applied to the leftmost block. What force does the middle block exert on the rightmost one?

A child pulls an 11-kg wagon with a horizontal handle whose mass is 1.8 kg, accelerating the wagon and handle at Find the tension forces at each end of the handle. Why are they different?

A 2200-kg airplane pulls two gliders, the first of mass 310 kg and the second of mass 260 kg, down the runway with acceleration (Fig. 4.22). Neglecting the mass of the two ropes and any frictional forces, determine (a) the horizontal thrust of the planes propeller; (b) the tension force in the first rope; (c) the tension force in the second rope; and (d) the net force on the first glider. 1.9 m/s2 2.3 m/s2.

A biologist is studying the growth of rats on the Space Station. To determine a rats mass, she puts it in a 320-g cage, attaches a spring scale, and pulls so that the scale reads 0.46 N. If rat and cage accelerate at whats the rats mass?

An elastic towrope has spring constant 1300 N/m. Its connected between a truck and a 1900-kg car. As the truck tows the car, the rope stretches 55 cm. Starting from rest, how far do the truck and the car move in 1 min? Assume the car experiences negligible friction.

A 2.0-kg mass and a 3.0-kg mass are on a horizontal frictionless surface, connected by a massless spring with spring constant k 5 140 N/m. A 15-N force is applied to the larger mass, as shown in Fig. 4.23. How much does the spring stretch from its equilibrium length?

Youre an automotive engineer designing the crumple zone of a new carthe region that compresses as the car comes to a stop in a head-on collision. If the maximum allowable force on a passenger in a 70-km/h collision is 20 times the passengers weight, what do you specify for the amount of compression in the crumple zone?

Frogs tongues dart out to catch insects, with maximum tongue accelerations of about What force is needed to give a 500-mg tongue such an acceleration?

Two large crates, with masses 640 kg and 490 kg, are connected by a stiff, massless spring and propelled along an essentially frictionless factory floor by a horizontal force applied to the more massive crate. If the spring compresses 5.1 cm, whats the applied force?

What force do the blades of a 4300-kg helicopter exert on the air when the helicopter is (a) hovering at constant altitude; (b) dropping at 21 m/s with speed decreasing at (c) rising at 17 m/s with speed increasing at (d) rising at a steady 15 m/s; (e) rising at 15 m/s with speed decreasing at

What engine thrust (force) is needed to accelerate a rocket of mass m (a) downward at near Earths surface; (b) upward at near Earths surface; (c) at in interstellar space, far from any star or planet?

Your engineering firm is asked to specify the maximum load for the elevators in a new building. Each elevator has mass 490 kg when empty and maximum acceleration The elevator cables can withstand a maximum tension of 19.5 kN before breaking. For safety, you need to ensure that the tension never exceeds two-thirds of that value. What do you specify for the maximum load? How many 70-kg people is that?

An F-16 jet fighter has mass 12 Mg and engine thrust 132 kN. An Airbus A-380 has mass 560 Mg and total engine thrust 1.5 MN. Could either aircraft climb vertically with no lift from its wings? If so, what vertical acceleration could it achieve?

Two springs have the same unstretched length but different spring constants, and (a) If theyre connected side by side and stretched a distance x, as shown in Fig. 4.24a, show that the force exerted by the combination is . (b) If theyre connected end to end (Fig. 4.24b) and the combination is stretched a distance x, show that they exert a force k1k2x/1k1 1 k22.

Although we usually write Newtons second law for onedimensional motion in the form which holds when mass is constant, a more fundamental version is F 5 . Consider an object whose mass is changing, and use the product rule for derivatives to show that Newtons law then takes the form .

A railroad car is being pulled beneath a grain elevator that dumps grain at the rate of 450 kg/s. Use the result of Problem 59 to find the force needed to keep the car moving at a constant 2.0 m/s.

A block 20% more massive than you hangs from a rope that goes over a frictionless, massless pulley. With what acceleration must you climb the other end of the rope to keep the block from falling?

Youre asked to calibrate a device used to measure vertical acceleration in helicopters. The device consists of a mass m hanging from a massless spring of constant k. Your job is to express the acceleration as a function of the springs stretch y from its equilibrium length. Whats your expression?

Your airplane is caught in a brief, violent downdraft. To your amazement, pretzels rise vertically off your seatback tray, and you estimate their upward acceleration relative to the plane at Whats the planes downward acceleration?

Youre assessing the Engineered Material Arresting System (EMAS) at New Yorks JFK airport. The system consists of a 132-m-long bed of crushable cement blocks, designed to stop aircraft from sliding off the runway in emergencies. The EMAS can exert a 300-kN force on a 55-Mg jetliner that hits the system at 36 m/s. Can it stop the plane before it plows through all the blocks?

Two masses are joined by a massless string. A 30-N force applied vertically to the upper mass gives the system a constant upward acceleration of If the string tension is 18 N, what are the two masses?

A mass M hangs from a uniform rope of length L and mass m. Find an expression for the rope tension as a function of the distance y measured downward from the top of the rope.

Jerk is the rate of change of acceleration, and its what can make you sick on an amusement park ride. In a particular ride, a car and passengers with total mass M are subject to a force given by , where and are constants. Find an expression for the maximum jerk.

At the first sign of turbulence, the planes acceleration a. is upward. b. is downward. c. is impossible to tell from the graph.

The planes vertical acceleration has its greatest magnitude a. during interval B. b. during interval C. c. during interval D.

During interval C, you can conclude for certain that the plane is a. at rest. b. accelerating upward. c. accelerating downward. d. moving with constant vertical velocity.

The magnitude of the greatest vertical acceleration the plane undergoes during the time shown on the graph is approximately