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Chapter 9: Answer Key

- The net force is zero since the mass is stationary.
- The upward tension of the rope must be enough to cancel out gravity.

- The horizontal component of tension T 2 must be bigger than the vertical component.
- The horizontal component of tension must be less than.
- The horizontal component of T 2 must be canceled by the horizontal rope T.

- The coefficient of static friction must be greater than the value since a greater force is needed.

- There are only two forces in the free-body diagram.

- The second law gives us a number.

- The first law says that inertia maintains its current motion once in motion.
- The vertical force of gravity is the only force on the ball after the throw.
- The ball's sideways velocity is maintained due to its inertia, because this causes the ball to accelerate in the vertical direction.

- The force pair of interaction between two objects is always equal according to the third law of action-reaction.
- The third law does not involve the acceleration of either object.
- The net force on a single object causes the acceleration.

- The net force is horizontal.

- The value is negative because it is to the left.
- The vertical forces have canceled out.

- An object in free fall will accelerate at a constant rate.
- Since the rock is already moving downward, there is an increase in speed of 9.8 m/s.
- The rock will fall much farther than 4.9 m as it is already moving close to 30 m/s downward by the start of the 3rd second.
- In the 4th second, it will fall an additional 35 meters.
- The rock does fall in the first second of the drop, but it falls more and more over time.

- The assumptions of the equations of motion are constant.
- Any permutation of signs or values will work in the equations of motion.
- One must use graphical methods if the acceleration is not constant.

- Projectile motion involves a constant vertical acceleration and no horizontal acceleration.
- Ax and ay are the same throughout the flight.
- There is no change in Vx since ax is zero.
- Vx is always the same.
- Vy is always changing.
- The projectile lands in the opposite direction so that Vyf is equal to Vyi.

- The motion of the objects has a correlation to their motion.
- If the inward force is released, the object will follow the law.
- After the object is released, gravity will cause it to fall, but the initial motion is horizontal.

- You can get this result by looking at the equation for orbital speed fromNewton.
- The square root of 2 shows that the Moon must decrease in speed.

- Regardless of location, mass is a property of the object.
- The object's mass and planetary gravity affect the weight of the object.

- The force is assumed to be equal to the weight of the object for most lifting operations.
- In order to get the suitcase moving faster, this brief force must be different in the second case.
- If the details of the forces contributing to the work are not easy to understand, you may want to think about the suitcase.

- The power must be supplied twice if the work is done in half the time.

- The mass's energy went up by 20 J.
- Since it was stationary, it had no KE.

- The collision is elastic and no energy is lost.

- The negative sign indicates that the impulse delivered to the ball is in the opposite direction.
- The ball and the wall receive the same impulses from the third law.

- Through the collision, total momentum must be maintained.
- The magnitude of the system's initial momentum is what we need to find.
- Each player is running in a straight line.
- Their individual momentums are different.
- The magnitude is found using the Pythagorean theorem.

- The lever arm has Force C applied to it.
- The force C has an angle of 180 degrees.

- Force A has a longer lever arm than force B.
- The Torque supplied by A is less than the Torque supplied by B.

- R 2 is the moment of inertia for a sphere.
- The moment of inertia has decreased because the shape of the cloud is not changing.

- The entire circuit needs to be shared between the two resistors.
- The split will be 50% since the two resistors are the same.

- The new resistor does not affect the original path because it forms its own parallel path.
- The same current will be drawn from the original Resistor since it has the same resistance and voltage.
- The current needs to be twice the current with the second resistor in place.

- electrons can move around the circuit if a switch is closed.
- The components within the circuit have electrons that start to flow.
- The movement of electrons within the bulb causes it to light up.
- The drift velocities of electrons in simple circuits are only about 0.03 cm/s.

- They emerge as if they had never met.
- The leading peak of the wave on the right will interfere with the leading trough of the wave on the left.
- The other half of the waves are unaffected by this partial destruction.
- When the waves are completely superposed, the trough will be on the peak of the waves.

- Wave speed is determined by the air.
- Waves won't be observed to be different by either observer.

- The wavelength needs to be higher in order to give the same speed.
- The higher frequencies are known as the Doppler shift.

- There is a difference in the velocities.

- There is an elastic collision between two objects.
- Net momentum is maintained by all collisions.
- The collision conserves energy.
- Equal but opposite exchanges of momentums are involved in all collisions.
- Inelastic collisions show that the energy is not conserved.

- This is a statics problem.

- Since the wedge is not moving, we are free to choose any axis of rotation we want.
- To eliminate one variable, we should place the axis of rotation at either contact point.

- This equation can be combined with the one above.

- The object has mass spread out over many different r values, so I cannot be used.

- At the lowest point of the downward swing, the angle between the lever arm and force goes from 90deg to 0deg.
- The Torque will decrease since it is proportional to the sin.

- This is a projectile motion problem.
- 55 percent of the initial energy is in potential energy.

- The time to fall is determined.

- To get time in flight, double this value.

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