SAMPLE TEST 2 FROM AU ‘11


1.  (52 POINTS) A  pilot takes off from a city in Northern California   and aims her airplane due North toward Seattle with a speed  240 km/h relative  to the air.   The air has an Eastward  wind of speed  100 km/h relative to the Earth. 

(a) (21 points) What is the magnitude of the airplane’s velocity relative to the Earth? 
(b) (21 points) What is the direction of the airplane’s velocity relative  to the Earth? Find  this direction by computing  the angle this  velocity makes with the North  direction shown in the schematic of the problem  below.
(c) (10 points) The airplane lands at a  small  airport  directly East of
Seattle. The north-south distance between the take off  location and Seattle is 1000 km.  How far East of Seattle does the airplane land? 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. (53 POINTS)  A person pushes  a crate rightward along a rough horizontal surface by pushing downward at 30 degrees below the horizontal with a force of magnitude F = 50.0 (N). The crate has mass  m = 10.0 kg.  See the diagram below.  Assume the coefficient of kinetic friction between the bottom of the crate and the surface is µk = 0.10.  

 

(a) (21 points) What is the magnitude N  of the normal force acting on the crate?   

(b) (32  points)  What is the horizontal acceleration ax of the crate?

 

 

 

 

 

 

 

 

 




 

 








3. (53 POINTS) Two blocks are connected by a light but sturdy  string wrapped around a mass-less pulley. The rough inclined surface makes an angle of 30 degrees with the horizontal. The block on the inclined surface has mass m = 5.0 kg. Assume the coefficient  of kinetic friction  between the  block of mass m  and the inclined plane is µk = 0.10.  The vertically hanging block has mass M = 50.0 kg. Assume the blocks begin their motion from rest.  

 

(a) (10 points) What is the magnitude N of the normal force on the block of mass m?  
(b) (5 points)  What direction does the hanging block move, up or down? Circle one.
(c) (18 points) What is the common magnitude a of the acceleration of the blocks? 
(d) (14 points) What is the magnitude T of the tension in the string?
(e) (6 points)   What is the speed of the hanging mass after it has moved a vertical distance of 1.50 m (assuming the hanging mass has not yet hit the ground and the block of mass m has not yet reached the upper edge of the incline)?

 

 

 

 

 

 

 

4. Extra Credit (9  points)

A 7.00-kg block slides along a  smooth hemispherical bowl of radius R = 1.0 m. The block starts from rest below the upper left edge of the bowl and slides toward the bottom. At the bottom the speed of the block is 4.00 m/s. At the bottom,

(a)  (2  points)  what is the direction of the block’s centripetal acceleration?  
(b)  (2 points)  what is the  magnitude the block’s  centripetal  acceleration? 
(c)  (5 points)  what is the magnitude N of the normal force on the block?

 

 

 

 


1.  (52 POINTS) A  pilot takes off from a city in Northern California   and aims her airplane due North toward Seattle with a speed  240 km/h relative  to the air.   The air has an Eastward  wind of speed  100 km/h relative to the Earth. 

(a) (21 points) What is the magnitude of the airplane’s velocity relative to the Earth? 
(b) (21 points) What is the direction of the airplane’s velocity relative  to the Earth? Find  this direction by computing  the angle this  velocity makes with the North  direction shown in the schematic of the problem  below.
(c) (10 points) The airplane lands at a  small  airport  directly East of
Seattle. The north-south distance between the take off  location and Seattle is 1000 km.  How far East of Seattle does the airplane land? 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. (53 POINTS)  A person pushes  a crate rightward along a rough horizontal surface by pushing downward at 30 degrees below the horizontal with a force of magnitude F = 50.0 (N). The crate has mass  m = 10.0 kg.  See the diagram below.  Assume the coefficient of kinetic friction between the bottom of the crate and the surface is µk = 0.10.  

 

(a) (21 points) What is the magnitude N  of the normal force acting on the crate?   

(b) (32  points)  What is the horizontal acceleration ax of the crate?

 

 

 

 

 

 

 

 

 




 

 








3. (53 POINTS) Two blocks are connected by a light but sturdy  string wrapped around a mass-less pulley. The rough inclined surface makes an angle of 30 degrees with the horizontal. The block on the inclined surface has mass m = 5.0 kg. Assume the coefficient  of kinetic friction  between the  block of mass m  and the inclined plane is µk = 0.10.  The vertically hanging block has mass M = 50.0 kg. Assume the blocks begin their motion from rest.  

 

(a) (10 points) What is the magnitude N of the normal force on the block of mass m?  
(b) (5 points)  What direction does the hanging block move, up or down? Circle one.
(c) (18 points) What is the common magnitude a of the acceleration of the blocks? 
(d) (14 points) What is the magnitude T of the tension in the string?
(e) (6 points)   What is the speed of the hanging mass after it has moved a vertical distance of 1.50 m (assuming the hanging mass has not yet hit the ground and the block of mass m has not yet reached the upper edge of the incline)?

 

 

 

 

 

 

 

4. Extra Credit (9  points)

A 7.00-kg block slides along a  smooth hemispherical bowl of radius R = 1.0 m. The block starts from rest below the upper left edge of the bowl and slides toward the bottom. At the bottom the speed of the block is 4.00 m/s. At the bottom,

(a)  (2  points)  what is the direction of the block’s centripetal acceleration?  
(b)  (2 points)  what is the  magnitude the block’s  centripetal  acceleration? 
(c)  (5 points)  what is the magnitude N of the normal force on the block?