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Chapter 78: Answer Key

- The average vertical velocity will be doubled.
- The product of these two is displacement.

- Since v at the maximum height is zero, one could use v 0 2 + 2 ad.
- The vertical displacement d must be four times bigger since v 0 is doubled and squared.

- Free-fall problems are not related to mass.

- The carts stick together.

- The max angle for range is equal between V X and V Y and will result in equal horizontal displacement.
- 30 degrees and 60 degrees are not the same as 45 degrees.

- 10 N is the maximum static friction.

- The object is not moving fast.

- It is possible to relate the height to the initial upward velocity.
- The bullet embedded in the wood will cause some unknown amount of mechanical energy to be lost.

- Ignore the minus sign when asked about magnitude.

- Since the final momentum must be zero, impulse equals change in momentum can be used.

- All other factors will only double the height.

- The existing 4-resistor is in close proximity to this 4- equivalent resistance.
- 2 is the equivalent resistance for that section of the circuit.
- The 2- equivalent resistance is in a series with the 3-resistor.

- The 3-amp current will split when it comes to the branching point.
- The current will split evenly since both pathways have equal resistance.

- The material is the same.

- The wavelength is the same.
- The higher wave speed must have caused the wave's frequencies to be raised.

- The velocities cannot be determined.
- The component of velocity not directed toward or away from the receiver does not contribute to the shift.

- 0.25 m is 25 cm.

- Equal length components would be included in a 45deg vector.
- The 45-45-90 triangles with their components would be formed by 135deg, 225deg, and 315deg.

- All values will decrease from maximum to minimum.

- The reading will be too high.

- The rolling object has to use some of the potential energy for rotational and linear energy.
- The object is moving slower down the hill.

- At the beginning and end of that single oscillation, the velocity is zero.
- Net work is not done because there is no change in energy.

- The wavelength of the standing wave is fixed by the length of the string.

- There will be a cancellation of the Torque caused by gravity on either side.

- The planet causes the weight of an object.
- The planet has a reaction force on it.
- The normal forces exchanged between the bottom surface of the book and the top surface of the table are an action-reaction pair.

- The average speed is greater from C to D.

- The slope of the line would be horizontal.
- The instantaneous velocity at this point is zero.

- The instantaneous velocity at these two points does not exist.
- Real-world motion is constant.

- Students should measure the period repeatedly and take the mean value.

- Take a period measurement for 5 to 10 different times and keep the mass and length the same.
- The string-mass combo can be pulled out to a certain angle by the protractor.

- Take a period measurement for 5 to 10 different mass.

- Take a period measurement for 5 to 10 different lengths.
- The center of mass is measured from the pivot point.

- Pendulums behave like simple harmonic oscillators under the conditions of small angles.
- The pendulum needs to be oscillated at larger angles.
- One can predict the results to deviate from the expected as the force no longer acts as a simple restorative force.

- The mass investigation could be a source of systematic error.
- The students may inadvertently be changing the length of the string when they add on different-sized mass.
- From the pivot point to the center of mass is the length of the pendulum.
- If the students did not compensate for this, they may see an artificial relationship at higher levels in their graph of mass versus period.

- The plot's slope would be equal to 4p 2 / g. One could plot T versus L.

- The slope is 4 s 2 /m.

- The mass will lose speed as it goes back up.
- The entire time the mass is inside the loop, it must be going through centripetal acceleration.
- The mass will fail to complete the loop if it is moving too slowly.
- The centripetal force is supplied by the normal force throughout the trajectory.
- A loss of contact between the sliding mass and the track is indicated if the normal force goes to zero.
- The top of the loop will have the slowest speed.
- This is the most likely place for the mass to fall.

- The right-hand side of the equation will be decreased as the speed at the top gets smaller.
- The normal force will be zero at some point when mv 2 / r gets small.
- The mass can complete the loop if the speed is greater than this.
- The mass will fail to complete the loop if the speed is lower.

- The top of the loop is where the potential energy is transformed into energy.
- The energy is proportional to the number.
- The centripetal force is linear with respect to the normal force.
- The critical speed is determined by the normal force going to zero.
- There is a linear dependence between h and r.

- A component of the force due to gravity is either centripetally or centrifugally.
- The normal force is acting alone at the points halfway between the top and bottom.

- The radial component of the two forces are shown in the drawings.

- The centripetal acceleration of the object is not possible because of the twinning components of gravity.

- The mechanical energy is being used.

- Less energy will be available for the tangential speed needed to make it through the loop since the original gravitational potential energy must now be going into rotational kinetic energy.
- The rolling object won't have enough energy to clear the top of the loop since the height was minimally set for the sliding block.

- The tension at point B will be higher than in case.
- The speed must be increased.

- The effect of the additional mass must be considered.
- The effective launch velocity will be affected by the rope's effect on mass.
- The end of the rope is the same as the object.
- At the center of the circle, the rest of the mass is moving at a lower speed.
- The net effect of the added mass is to decrease the launch velocity.
- The center of mass of an object is tracked by the equations of motion.
- The combined rope-plus-object system is being launched from a lower height since the center of mass is lower.
- A shorter range for the projectile is caused by a lower launch velocity.

- This negative work is done by the component of weight that is tangent.
- The tension must do some positive work to maintain the same energy.
- The circle can't be perfect because the tension must supply an upward component as well.
- Positive and negative work roles must reverse on the downward half of the circular motion.

- If there was resistance, there would be losses in our circuit.
- When modeling actual resistance inside of components, a "Internal" Resistor is added to the circuit diagram.

- If they didn't have infinite resistance, they would create a parallel path.
- If they have less than infinite resistance, the addition of voltmeters to the circuit would lower the resistance.

- An example of this is to start at the right of the power supply and then trace a loop clockwise through the top parallel resistor and back to our starting point.

- The current measured by the ammeter is reduced by this.

- If you have one of the two answers correct, the questions will be graded as completely correct (1 point) or incorrect (0 points).

- Any correct responses within an individual free-response question will be awarded partial credit.

- The guidelines above are based on the scores from the past AP Physics 1 exams.
- The actual score ranges are determined by the College Board each year.
- The ranges shown are approximations.

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