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Describe several situations in which an object is not in equilibrium, even though the net force on it is zero.
- An example would be using a wrench to turn a bolt. The force is pulling from one side and pushing from the other (going in opposite directions) and so the net force would be zero, however, because of the difference in torque, the bolt would rotate.
- Transitional and Rotational Equilibrium
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A bungee jumper momentarily comes to rest at the bottom of the dive before he springs back upward. At that moment, is the bungee jumper in equilibrium? Explain.
- The rope of bungee jumping is like a spring. When the net force acting on an object is zero the object is said to be in translational equilibrium. The bungee jumping rope is like a spring. When the load is suspended, the rope stretches until the net force acting on the object is zero. When the weight of the object W and restoring force of the spring F is equal the object comes to rest. This point is the lowest point of the bungee jumper, there the object is in equilibrium.
- No, because there is a net force acting on him. The rope's tension is actually greater than his own weight, and that's why in the next instant he's aquired an upwards acceleration. The only thing significant about the bottom of the dive is that in that instant, the net force is zero (0), but the object still has acceleration which results in a change of velocity. The jumper has a net upward force when at the bottom of the dive, and that is why the jumper is then pulled back upwards.
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You can find the center of gravity of a meter stick by resting it horizontally on your two index fingers,and then slowly drawing your fingers together. First the meter stick will slip on one finger, and then on the other, but eventually the fingers meet at the CG. Why does this work?
- If the fingers are not the same distance from the CG, the finger closer to the CG will support a larger fraction of the weight of the meter stick so that the net torque on the stick is zero. That larger vertical force means there will be more friction between the stick and that closer finger, and thus the finger further from the CG will be easier to move. The more distant finger will slide easier, and therefore move in closer to the CG. That finger, when it becomes the one closest to the CG, will then have more friction and will "stick". The other finger will then slide. You then repeat the process. Whichever finger is farther from the CG will slide closer to it, until the two fingers eventually meet at the CG.
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- A ground retaining wall is shown in Fig.9–36a. The ground, particularly when wet, can exert a significant force F on the wall. (a) What force produces the torque to keep the wall upright? (b) Explain why the retaining wall in Fig. 9–36b would be much less likely to overturn than that in Fig.9–36a.
- (a) The weight of the wall exerts the torque to keep it upright. (b) The lever arm for the wall in (a) is small (half the width of the wall) so the torque due to its weight is small. For the wall in (b), in addition to the weight of the wall there is a torque due to the weight of horizontal part of the wall and the soil above it. This is a much larger force and has a much larger lever arm so the horizontal force exerted by the ground on the vertical part of the wall would have to be many tines larger in order to overturn it,
- a) Let us assume that in this case, the pivot point is the lower left corner of the wall as shown in the figure, then in that case the gravity force acting through the CM actually provides the required torque to keep the wall upright. It is very important to note that gravity force would always have a small lever arm which is approximately half (1/2) the width of the wall and hence the sideways force accutually could not have to be large to start to move the wall. b) With the horizontal extension as indicated in th eFig 9-36 b, following are the factors that actually make the wall less likely to overturn: 1) Because of horizontal extension the actuall mass of the second (2nd) wall would be larger and because of the this the...
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A ladder, leaning against a wall, makes a 60° angle with the ground. When is it more likely to slip: when a person stands on the ladder near the top or near the bottom? Explain.
- Certainly at the top. The downward force of gravity is pulling you straight down, Since the force of that gravity is then transferred to the bottom of the ladder, that force is an angular force pushing out from the center of gravity. The higher up you go, the greater the center of gravity becomes.
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- A ladder leans against a frictionless wall. When is it more likely to slip: when a person stands near the top or near the bottom? Explain. The ladder is more likely to slip when a person stands near the top. Consider the torques about point A. To be in static equilibrium, the torque produced by Ff'n, the normal force from the wall, must be balanced by the torques produced by mq, the weight of the ladder, and Mi], the weight of the person. If the person is near the top of the ladder, the torque produced by M fJ is larger than when they are near the bottom, J:.~V2 must therefore be larger when the person is near the top of the ladder. [~r for static equilibrium so the largest frictional force is required when the person is near the top. The ladder will slip if the limit of static friction Ffr = /l,,,F'Nl is exceeded, where Fm is the normal force from the ground, 1"8 is the coefficient of static friction, and Ffr is the frictional force. Note that FNl = /7I,g ## +j{g doesn't change as the person moves up the ladder so the limit of static friction doesn't change during the climb.
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A uniform meter stick supported at the 25-cm mark is in equilibrium when a 1-kg rock is suspended at the 0-cm end (as shown in Fig.9–37). Is the mass of the meter stick greater than, equal to, or less than the mass of the rock? Explain your reasoning.
- The mass of the meter stick is 1 kg. The system is in equilibrium, so the torques must be balanced. The center of gravity of the stick is at the 50 cm mark and the fulcrum is in the middle of that, at the 25 cm mark, and since the weight is all concentrated at the center of gravity, the weight of the rock must be the same as the weight of the stick in order to produce the same torque, since the lever arms are both 25 cm.
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Why do you tend to lean backward when carrying a heavy load in your arms? * When walking, you must keep your CG over your feet. If you have a heavy load in your arms, your CG is shifted forward, and so you must lean backwards to realign your CG over your feet.
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Which configuration of bricks, Fig. 9–39a or Fig. 9–39b, is the more likely to be stable? Why?
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You have two springs that are identical except that spring 1 is stiffer than spring 2. On which spring is more work done: (a) if they are stretched using the same force; (b) if they are stretched the same distance?
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If the speed of a particle triples, by what factor does its kinetic energy increase?
- Kinetic energy = (1/2) (mass) (speed)² . See that little ² there on the end ? That tells us that kinetic energy is proportional to the square of the speed. If the speed of the moving object triples, then the moving object has 3² or nine times as much kinetic energy as it had before. A better way to look at it is: If you want to triple the speed of a moving object, it's not enough to just give it 3 times as much kinetic energy as it has now. You have to give it 9 times as much as it has now.
- The kinetic energy increases by a factor of 9, since kinetic energy is proportional to the square of the speed.
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Two identical arrows, one with twice the speed of the other are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster arrow will penetrate how much farther than the slow arrow? Explain using Work and Energy equations.
- The faster arrow has the same mass and twice the speed of the slower arrow, so the faster arrow will have four times the kinetic energy. Therefore, four times as much work must be done on the faster arrow to bring it to rest. If the force on the arrows is constant, the faster arrow will travel four times the distance of the slower arrow into the hay.
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What happens to the gravitational potential energy when water at the top of a waterfall falls to the pool below?
- When water at the top of a waterfall falls to the pool below, initially the water's gravitational PE is turned into kinetic energy. That kinetic energy then can do work on the pool water when it hits it, and so some of the pool water is given energy, which makes it splash upwards and outwards and creates outgoing water waves, which carry energy. Some of the energy will become heat, due to viscous friction between the falling water and the pool water. Some of the energy will become kinetic energy of air molecules, making sound waves that give the waterfall its "roar".
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Experienced hikers prefer to step over a fallen log in their path rather than stepping on top and stepping down on the other side. Why?
- it take no work step over the log, if you step on the log you will gave to do work lifting your weight
- By stepping over the log they are conserving energy. By stepping up onto the log they would have to expend energy to raise the mass of their body to the height of the log (create potential energy) and then expend the potential energy by jumping to the ground.
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Describe the energy transformations that take place when a skier starts skiing down a hill, but after a time is brought to rest by striking a snowdrift.
- The skier will transform their gravitational energy into mostly kinetic energy (with a minor amount transformed into heat from the friction of the skis across the snow and air friction) . Once the skier hits the snowdrift, their kinetic energy is transferred into the snow which moves when they strike it due to the kinetic energy that is now in the snow. Along with again a minor amount of heat energy transferred as they move through the snowdrift.
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Describe the energy transformations when a child hops around on a pogo stick (there is a spring inside).
- Start the description with the child suspended in mid-air, at the top of a hop. All of the energy is gravitational PE at that point. Then, the child falls, and gains kinetic energy. When the child reaches the ground, most of the energy is kinetic. As the spring begins to compress, the kinetic energy is changed into elastic PE. The child also goes down a little bit further as the spring compresses, and so more gravitational PE is also changed into elastic PE. At the very bottom of a hop, the energy is all elastic PE. Then as the child rebounds, the elastic PE is turned into kinetic energy and gravitational PE. When the child reaches the top of the bounce, all of the elastic PE has been changed into gravitational PE, because the child has a speed of 0 at the top. Then the cycle starts over again. Due to friction, the child must also add energy to the system by pushing down on the pogo stick while it is on the ground, getting a more forceful reaction from the ground.
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Suppose you lift a suitcase from the floor to table. The work you do on the suitcase depends on which of the following: a)whether you lift straight up or along a more complicated path, b) the time it takes, c) the height of the table, and d) the weight of the suitcase.
- The work you do is only dependent on the weight of the suitcase and the height of the table because work is equal to mgy, where y is solely the displacement in the vertical direction because it is in the same direction as the applied force.
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- Why is it easier to climb a mountain via a zigzag trail than to climb straight up.
- The climber does the same amount of work whether climbing straight up or via a zig-zag path, ignoring dissipative forces. But if a longer zig-zag path is taken, it takes more time to do the work, and so the power output needed from the climber is less. That will make the climb easier. It is easier for the human body to generate a small amount of power for long periods of time rather than to generate a large power for a small period of time.