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Homework 8

Homework 8 - homework 08 BAUTISTA ALDO Due Feb 8 2006 4:00...

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homework 08 – BAUTISTA, ALDO – Due: Feb 8 2006, 4:00 am 1 Version number encoded for clicker entry: V1:1, V2:4, V3:2, V4:4, V5:3. Question 1 Part 1 of 2. 10 points. Three objects can only move along a straight, level path. The graphs below show the position d of each of the objects plotted as a function of time t . d t I d t II d t III The magnitude of the velocity k ~v k of the object increases in which of the cases? 1. I, II, and III 2. II and III only 3. III only correct 4. I and III only 5. I only 6. I and II only 7. II only Explanation: Case I: The object moves at constant speed. Case II: The object remains at rest. Case III: The speed of the object increases with time; i.e. , constant acceleration. Thus, the magnitude of the velocity of the object increases only in case III. Question 2 Part 2 of 2. 10 points. The sum of the forces X F i = 0 on the object is zero in which of the cases? 1. I and II only correct 2. I only 3. III only 4. I, II, and III 5. II and III only 6. II only 7. I and III only Explanation: When the sum of forces on the object is zero, the acceleration of object is zero by Newton’s 2nd law. In cases I and II, the velocity of the object doesn’t change with the time, so the sum of the forces on the object is zero. In case III, the object is accelerating, so the sum of forces on the object is not zero. Question 3 Part 1 of 1. 10 points. A block of mass m accelerates with acceler- ation g up a frictionless plane that is inclined at an angle α above the horizontal. The force F o that pushes the block is at an angle β above the horizontal. Find the force F o . m α β F o 1. m g 1 + sin α cos( β - α ) 2. m g 1 cos( α + β ) 3. m g 1 - sin β cos( β - α ) 4. m g 1 - sin β cos( α + β )

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homework 08 – BAUTISTA, ALDO – Due: Feb 8 2006, 4:00 am 2 5. m g 1 + sin β cos( β - α ) 6. m g 1 + sin α cos( α + β ) correct 7. m g 1 + sin β cos( α - β ) 8. m g 1 + sin β cos( α + β ) 9. m g sin β cos( α + β ) 10. m g 1 + sin α cos( α - β ) Explanation: The acceleration up the plane is given, a = g . The angle that F o makes with respect to the inclined plane is α + β . So the component of F o which is parallel to the inclined plane is F o cos( α + β ) Therefore F o cos( α + β ) - m g sin
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