Chapter 4: Q3CQ (page 159)
How are inertia and mass related?
The object with more mass has more inertia. Inertia is directly proportional to the mass of the body.
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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 N on the car if the angle is 2.00°? 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° and you still apply the force found in part (a) to its center?
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.
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.
(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?
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.
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