Integrated Concepts When starting a foot race, a 70.0-kg

Problem 54PE What is the ratio of the strength of the strong nuclear force to that of the electromagnetic force? Based on this ratio, you might expect that the strong force dominates the nucleus, which is true for small nuclei. Large nuclei, however, have sizes greater than the range of the strong nuclear force. At these sizes, the electromagnetic force begins to affect nuclear stability. These facts will be used to explain nuclear fusion and fission later in this text.

Problem 1CQ Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.

Problem 1PE A 63.0-kg sprinter starts a race with an acceleration of 4.20 m/s2 . What is the net external force on him?

Problem 2CQ What properties do forces have that allow us to classify them as vectors?

Problem 2PE If the sprinter from the previous problem accelerates at that rate for 20 m, and then maintains that velocity for the remainder of the 100-m dash, what will be his time for the race?

Problem 3CQ How are inertia and mass related?

Problem 4CQ What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?

Problem 3PE A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate the magnitude of its acceleration.

Problem 4PE Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be 0.893 m/s2. (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which recoil of the vehicle is avoided.

Problem 5CQ Which statement is correct? (a) Net force causes motion. (b) Net force causes change in motion. Explain your answer and give an example.

In Figure \(4.7\), the net external force on the \(\text { 24-kg }\) mower is stated to be \(51 \mathrm{~N}\). If the force of friction opposing the motion is \(24 \mathrm{~N}\), what force \(F\) (in newtons) is the person exerting on the mower? Suppose the mower is moving at \(1.5 \mathrm{~m} / \mathrm{s}\) when the force \(F\) is removed. How far will the mower go before stopping? Equation Transcription: Text Transcription: 4.7 24-kg 51 N 24 N F 1.5 m/s

Problem 6CQ Why can we neglect forces such as those holding a body together when we apply Newton’s second law of motion?

The same rocket sled drawn in Figure \(4.31\) is decelerated at a rate of \(196 \mathrm{~m} / \mathrm{s}^{2}\) . What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is \(2100 kg\). Equation Transcription: Text Transcription: 4.31 196 m/s^2 2100 kg

Problem 7CQ Explain how the choice of the “system of interest” affects which forces must be considered when applying Newton’s second law of motion.

a) If the rocket sled shown in Figure \(4.32\) starts with only one rocket burning, what is the magnitude of its acceleration? Assume that the mass of the system is \(2100 kg\), the thrust \(T\) is \(2.4 \times 10^{4} \mathrm{~N}\), and the force of friction opposing the motion is known to be \(650 N\). (b) Why is the acceleration not one-fourth of what it is with all rockets burning? Equation Transcription: Text Transcription: 4.32 2100 kg T 2.4 times 10^4 N 650 N

Problem 8CQ Describe a situation in which the net external force on a system is not zero, yet its speed remains constant.

Problem 8PE What is the deceleration of the rocket sled if it comes to rest in 1.1 s from a speed of 1000 km/h? (Such deceleration caused one test subject to black out and have temporary blindness.)

Problem 9CQ A system can have a nonzero velocity while the net external force on it is zero. Describe such a situation.

Problem 9PE Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg. (a) What is the system of interest if the acceleration of the child in the wagon is to be calculated? (b) Draw a free-body diagram, including all forces acting on the system. (c) Calculate the acceleration. (d) What would the acceleration be if friction were 15.0 N?

Problem 10CQ A rock is thrown straight up. What is the net external force acting on the rock when it is at the top of its trajectory?

Problem 10PE A powerful motorcycle can produce an acceleration of 3.50 m/s2 while traveling at 90.0 km/h. At that speed the forces resisting motion, including friction and air resistance, total 400 N. (Air resistance is analogous to air friction. It always opposes the motion of an object.) What is the magnitude of the force the motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg?

Problem 11CQ (a) Give an example of different net external forces acting on the same system to produce different accelerations. (b) Give an example of the same net external force acting on systems of different masses, producing different accelerations. (c) What law accurately describes both effects? State it in words and as an equation.

The rocket sled shown in Figure \(4.33\) accelerates at a rate of \(49.0 \mathrm{~m} / \mathrm{s}^{2}\) . Its passenger has a mass of \(75.0 \mathrm{~kg}\). (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight by using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body. Equation Transcription: Text Transcription: 4.33 49.0 m/s^2 75.0 kg

Problem 12CQ If the acceleration of a system is zero, are no external forces acting on it? What about internal forces? Explain your answers.

Repeat the previous problem for the situation in which the rocket sled decelerates at a rate of \(201 \mathrm{~m} / \mathrm{s}^{2}\) . In this problem, the forces are exerted by the seat and restraining belts. Equation Transcription: Text Transcription: 201 m/s^2

Problem 13CQ If a constant, nonzero force is applied to an object, what can you say about the velocity and acceleration of the object?

Problem 13PE The weight of an astronaut plus his space suit on the Moon is only 250 N. How much do they weigh on Earth? What is the mass on the Moon? On Earth?

Problem 14CQ The gravitational force on the basketball in Figure 4.6 is ignored. When gravity is taken into account, what is the direction of the net external force on the basketball—above horizontal, below horizontal, or still horizontal?

Problem 14PE Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 10,000 kg. The thrust of its engines is 30,000 N. (a) Calculate its the magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.

Problem 15CQ When you take off in a jet aircraft, there is a sensation of being pushed back into the seat. Explain why you move backward in the seat—is there really a force backward on you? (The same reasoning explains whiplash injuries, in which the head is apparently thrown backward.)

Problem 15PE What net external force is exerted on a 1100-kg artillery shell fired from a battleship if the shell is accelerated at 2.40×104 m/s2 ? What is the magnitude of the force exerted on the ship by the artillery shell?

Problem 16CQ A device used since the 1940s to measure the kick or recoil of the body due to heart beats is the “ballistocardiograph.” What physics principle(s) are involved here to measure the force of cardiac contraction? How might we construct such a device?

Problem 16PE A brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 N on him. The mass of the losing player plus equipment is 90.0 kg, and he is accelerating at 1.20 m/s2 backward. (a) What is the force of friction between the losing player’s feet and the grass? (b) What force does the winning player exert on the ground to move forward if his mass plus equipment is 110 kg? (c) Draw a sketch of the situation showing the system of interest used to solve each part. For this situation, draw a free-body diagram and write the net force equation.

Describe a situation in which one system exerts a force on another and, as a consequence, experiences a force that is equal in magnitude and opposite in direction. Which of Newton’s laws of motion apply?

Problem 17PE Two teams of nine members each engage in a tug of war. Each of the first team’s members has an average mass of 68 kg and exerts an average force of 1350 N horizontally. Each of the second team’s members has an average mass of 73 kg and exerts an average force of 1365 N horizontally. (a) What is magnitude of the acceleration of the two teams? (b) What is the tension in the section of rope between the teams?

Problem 18CQ Why does an ordinary rifle recoil (kick backward) when fired? The barrel of a recoilless rifle is open at both ends. Describe how Newton’s third law applies when one is fired. Can you safely stand close behind one when it is fired?

Problem 18PE What force does a trampoline have to apply to a 45.0-kg gymnast to accelerate her straight up at 7.50 m/s2 ? Note that the answer is independent of the velocity of the gymnast—she can be moving either up or down, or be stationary.

An American football lineman reasons that it is senseless to try to out-push the opposing player, since no matter how hard he pushes he will experience an equal and opposite force from the other player. Use Newton’s laws and draw a free-body diagram of an appropriate system to explain how he can still out-push the opposition if he is strong enough.

Problem 19PE (a) Calculate the tension in a vertical strand of spider web if a spider of mass 8.00×10?5 kg hangs motionless on it. (b) Calculate the tension in a horizontal strand of spider web if the same spider sits motionless in the middle of it much like the tightrope walker in Figure 4.17. The strand sags at an angle of 12º below the horizontal. Compare this with the tension in the vertical strand (find their ratio).

Problem 20CQ Newton’s third law of motion tells us that forces always occur in pairs of equal and opposite magnitude. Explain how the choice of the “system of interest” affects whether one such pair of forces cancels.

Problem 20PE Suppose a 60.0-kg gymnast climbs a rope. (a) What is the tension in the rope if he climbs at a constant speed? (b) What is the tension in the rope if he accelerates upward at a rate of 1.50 m/s2 ?

If a leg is suspended by a traction setup as shown in Figure \(4.30\), what is the tension in the rope? Figure \(4.30\) A leg is suspended by a traction system in which wires are used to transmit forces. Frictionless pulleys change the direction of the force \(T\) without changing its magnitude. Equation Transcription: Text Transcription: 4.30 T

Show that, as stated in the text, a force \(F_{\perp}\) exerted on a flexible medium at its center and perpendicular to its length (such as on the tightrope wire in Figure \(4.17\) ) gives rise to a tension of magnitude \(T=\frac{F_{\perp}}{2 \sin (\theta)}\) Equation Transcription: Text Transcription: F_prep 4.17 T = F_prep/2 sin (theta)

Consider the baby being weighed in Figure \(4.34\). (a) What is the mass of the child and basket if a scale reading of \(55 N\) is observed? (b) What is the tension \(T_{1}\) in the cord attaching the baby to the scale? (c) What is the tension \(T_{2}\) in the cord attaching the scale to the ceiling, if the scale has a mass of \(0.500 \mathrm{~kg}\)? (d) Draw a sketch of the situation indicating the system of interest used to solve each part. The masses of the cords are negligible. Figure \(4.34\) A baby is weighed using a spring scale. Equation Transcription: Text Transcription: 4.34 55 N T_1 T_2 0.500 kg

Problem 23CQ To simulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at g. Why will they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference between their apparent weightlessness in orbit and in the aircraft?

Problem 23PE A 5.00×105 -kg rocket is accelerating straight up. Its engines produce 1.250×107 N of thrust, and air resistance is 4.50×106 N . What is the rocket’s acceleration? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

Problem 24CQ A cartoon shows the toupee coming off the head of an elevator passenger when the elevator rapidly stops during an upward ride. Can this really happen without the person being tied to the floor of the elevator? Explain your answer.

Problem 24PE The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 250 N and the acceleration of the car is 1.80 m/s2 , what is the mass of the car plus its occupants? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. For this situation, draw a free-body diagram and write the net force equation.

Problem 25CQ Explain, in terms of the properties of the four basic forces, why people notice the gravitational force acting on their bodies if it is such a comparatively weak force.

Problem 25PE Calculate the force a 70.0-kg high jumper must exert on the ground to produce an upward acceleration 4.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

Problem 26CQ What is the dominant force between astronomical objects? Why are the other three basic forces less significant over these very large distances?

Problem 26PE When landing after a spectacular somersault, a 40.0-kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 7.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion.

Problem 27CQ Give a detailed example of how the exchange of a particle can result in an attractive force. (For example, consider one child pulling a toy out of the hands of another.)

A freight train consists of two 8.00×104 -kg engines and 45 cars with average masses of 5.50×104 kg . (a) What force must each engine exert backward on the track to accelerate the train at a rate of 5.00×10–2 m/s2 if the force of friction is 7.50×105 N , assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (b) What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?

Problem 28PE Commercial airplanes are sometimes pushed out of the passenger loading area by a tractor. (a) An 1800-kg tractor exerts a force of 1.75×104 N backward on the pavement, and the system experiences forces resisting motion that total 2400 N. If the acceleration is 0.150 m/s2, what is the mass of the airplane? (b) Calculate the force exerted by the tractor on the airplane, assuming 2200 N of the friction is experienced by the airplane. (c) Draw two sketches showing the systems of interest used to solve each part, including the free-body diagrams for each.

Problem 29PE A 1100-kg car pulls a boat on a trailer. (a) What total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-N force on the road and produces an acceleration of 0.550 m/s2 ? The mass of the boat plus trailer is 700 kg. (b) What is the force in the hitch between the car and the trailer if 80% of the resisting forces are experienced by the boat and trailer?

(a) Find the magnitudes of the forces \(\mathbf{F}_{1}\) and \(\mathbf{F}_{2}\) that add to give the total force \(F_{\text {tot }}\) shown in Figure \(4.35\). This may be done either graphically or by using trigonometry. (b) Show graphically that the same total force is obtained independent of the order of addition of \(\mathbf{F}_{1}\) and \(\mathbf{F}_{2}\) . (c) Find the direction and magnitude of some other pair of vectors that add to give \(F_{\text {tot }}\) . Draw these to scale on the same drawing used in part (b) or a similar picture. Equation Transcription: Text Transcription: F_1 F_2 F_tot 4.35

Suppose your car was mired deeply in the mud and you wanted to use the method illustrated in Figure \(4.37\) to pull it out. (a) What force would you have to exert perpendicular to the center of the rope to produce a force of \(12,000 \mathrm{~N}\) on the car if the angle is \(2.00^{\circ}\)? In this part, explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. (b) Real ropes stretch under such forces. What force would be exerted on the car if the angle increases to \(7.00^{\circ}\) and you still apply the force found in part (a) to its center? Equation Transcription: Text Transcription: 4.37 12,000 N 2.00 degrees 7.00 degrees

What force is exerted on the tooth in Figure \(4.38\) if the tension in the wire is \(25.0 \mathrm{~N}\)? Note that the force applied to the tooth is smaller than the tension in the wire, but this is necessitated by practical considerations of how force can be applied in the mouth. Explicitly show how you follow steps in the Problem-Solving Strategy for Newton’s laws of motion. Figure \(4.38\) Braces are used to apply forces to teeth to realign them. Shown in this figure are the tensions applied by the wire to the protruding tooth. The total force applied to the tooth by the wire, \(\mathrm{F}_{\mathrm{app}}\) , points straight toward the back of the mouth. Equation Transcription: Text Transcription: 4.38 25.0 N F_app

Figure \(4.39\) shows Superhero and Trusty Sidekick hanging motionless from a rope. Superhero’s mass is \(90.0 \mathrm{~kg}\), while Trusty Sidekick’s is \(55.0 \mathrm{~kg}\), and the mass of the rope is negligible. (a) Draw a free-body diagram of the situation showing all forces acting on Superhero, Trusty Sidekick, and the rope. (b) Find the tension in the rope above Superhero. (c) Find the tension in the rope between Superhero and Trusty Sidekick. Indicate on your free-body diagram the system of interest used to solve each part. Figure \(4.39\) Superhero and Trusty Sidekick hang motionless on a rope as they try to figure out what to do next. Will the tension be the same everywhere in the rope? Equation Transcription: Text Transcription: 4.39 90.0 kg 55.0 kg

Two children pull a third child on a snow saucer sled exerting forces \(\mathbf{F}_{1}\) and \(\mathbf{F}_{2}\) as shown from above in Figure \(4.36\). Find the acceleration of the \(49.00-\mathrm{kg}\) sled and child system. Note that the direction of the frictional force is unspecified; it will be in the opposite direction of the sum of \(\mathbf{F}_{1}\) and \(\mathbf{F}_{2}\) . Figure \(4.36\) An overhead view of the horizontal forces acting on a child’s snow saucer sled. Equation Transcription: Text Transcription: F_1 F_2 4.36 49.00-kg

Problem 35PE A nurse pushes a cart by exerting a force on the handle at a downward angle 35.0º below the horizontal. The loaded cart has a mass of 28.0 kg, and the force of friction is 60.0 N. (a) Draw a free-body diagram for the system of interest. (b) What force must the nurse exert to move at a constant velocity?

Problem 36PE Construct Your Own Problem Consider the tension in an elevator cable during the time the elevator starts from rest and accelerates its load upward to some cruising velocity. Taking the elevator and its load to be the system of interest, draw a free-body diagram. Then calculate the tension in the cable. Among the things to consider are the mass of the elevator and its load, the final velocity, and the time taken to reach that velocity.

Problem 37PE Construct Your Own Problem Consider two people pushing a toboggan with four children on it up a snowcovered slope. Construct a problem in which you calculate the acceleration of the toboggan and its load. Include a freebody diagram of the appropriate system of interest as the basis for your analysis. Show vector forces and their components and explain the choice of coordinates. Among the things to be considered are the forces exerted by those pushing, the angle of the slope, and the masses of the toboggan and children.

Problem 38PE Unreasonable Results (a) Repeat Exercise 4.29, but assume an acceleration of 1.20 m/s2 is produced. (b) What is unreasonable about the result? (c) Which premise is unreasonable, and why is it unreasonable? Exercise 4.29: A 1100-kg car pulls a boat on a trailer. (a) What total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-N force on the road and produces an acceleration of 0.550 m/s2 ? The mass of the boat plus trailer is 700 kg. (b) What is the force in the hitch between the car and the trailer if 80% of the resisting forces are experienced by the boat and trailer?

Problem 40PE A flea jumps by exerting a force of 1.20×10?5 N straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of 0.500×10?6 N on the flea. Find the direction and magnitude of the acceleration of the flea if its mass is 6.00×10?7 kg . Do not neglect the gravitational force.

Problem 39PE Unreasonable Results (a) What is the initial acceleration of a rocket that has a mass of 1.50×106 kg at takeoff, the engines of which produce a thrust of 2.00×106 N ? Do not neglect gravity. (b) What is unreasonable about the result? (This result has been unintentionally achieved by several real rockets.) (c) Which premise is unreasonable, or which premises are inconsistent? (You may find it useful to compare this problem to the rocket problem earlier in this section.)

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in Figure \(4.40\). (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by this force? Figure \(4.40\) Achilles tendon Equation Transcription: Text Transcription: 4.40

A \(\text { 76.0-kg }\) person is being pulled away from a burning building as shown in Figure \(4.41\). Calculate the tension in the two ropes if the person is momentarily motionless. Include a free-body diagram in your solution. Figure \(4.41\) The force \(\mathrm{T}_{2}\) needed to hold steady the person being rescued from the fire is less than her weight and less than the force \(\mathrm{T}_{1}\) in the other rope, since the more vertical rope supports a greater part of her weight (a vertical force). Equation Transcription: Text Transcription: 76.0-kg 4.41 T_2 T_1

Problem 43PE Integrated Concepts A 35.0-kg dolphin decelerates from 12.0 to 7.50 m/s in 2.30 s to join another dolphin in play. What average force was exerted to slow him if he was moving horizontally? (The gravitational force is balanced by the buoyant force of the water.)

Problem 44PE Integrated Concepts When starting a foot race, a 70.0-kg sprinter exerts an average force of 650 N backward on the ground for 0.800 s. (a) What is his final speed? (b) How far does he travel?

Problem 45PE Integrated Concepts A large rocket has a mass of 2.00×106 kg at takeoff, and its engines produce a thrust of 3.50×107 N . (a) Find its initial acceleration if it takes off vertically. (b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust? (c) In reality, the mass of a rocket decreases significantly as its fuel is consumed. Describe qualitatively how this affects the acceleration and time for this motion.

Problem 46PE Integrated Concepts A basketball player jumps straight up for a ball. To do this, he lowers his body 0.300 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.900 m above the floor. (a) Calculate his velocity when he leaves the floor. (b) Calculate his acceleration while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.300 m. (c) Calculate the force he exerts on the floor to do this, given that his mass is 110 kg.

Problem 47PE Integrated Concepts A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m. (a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar. (b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as it goes from zero to the velocity found in (a). (c) What is the average force on the shell in the mortar? Express your answer in newtons and as a ratio to the weight of the shell.

Problem 48PE Integrated Concepts Repeat Exercise 4.47 for a shell fired at an angle 10.0º from the vertical. Exercise 4.47: Integrated Concepts A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m. (a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar. (b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as it goes from zero to the velocity found in (a). (c) What is the average force on the shell in the mortar? Express your answer in newtons and as a ratio to the weight of the shell.

Problem 49PE Integrated Concepts An elevator filled with passengers has a mass of 1700 kg. (a) The elevator accelerates upward from rest at a rate of 1.20 m/s2 for 1.50 s. Calculate the tension in the cable supporting the elevator. (b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time? (c) The elevator decelerates at a rate of 0.600 m/s2 for 3.00 s. What is the tension in the cable during deceleration? (d) How high has the elevator moved above its original starting point, and what is its final velocity?

Problem 51PE Unreasonable Results A 75.0-kg man stands on a bathroom scale in an elevator that accelerates from rest to 30.0 m/s in 2.00 s. (a) Calculate the scale reading in newtons and compare it with his weight. (The scale exerts an upward force on him equal to its reading.) (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?

Problem 50PE Unreasonable Results (a) What is the final velocity of a car originally traveling at 50.0 km/h that decelerates at a rate of 0.400 m/s2 for 50.0 s? (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?

Problem 52PE (a) What is the strength of the weak nuclear force relative to the strong nuclear force? (b) What is the strength of the weak nuclear force relative to the electromagnetic force? Since the weak nuclear force acts at only very short distances, such as inside nuclei, where the strong and electromagnetic forces also act, it might seem surprising that we have any knowledge of it at all. We have such knowledge because the weak nuclear force is responsible for beta decay, a type of nuclear decay not explained by other forces.

Problem 53PE (a) What is the ratio of the strength of the gravitational force to that of the strong nuclear force? (b) What is the ratio of the strength of the gravitational force to that of the weak nuclear force? (c) What is the ratio of the strength of the gravitational force to that of the electromagnetic force? What do your answers imply about the influence of the gravitational force on atomic nuclei?