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Physics 140 Test #4 1) A proton moves at 2

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Physics 140 Test #4

1) A proton moves at 2.5 x 10⁶ m/s rightwards when it encounters a region where there is uniform magnetic field of magnitude 3.2 x 10^-3 T confined to a rectangular region and directed perpendicular to the page. The proton undergoes a semicircular trajectory and exits the field.

 

1. Determine the length of the semicircular path. (1 mark)
2. What is the direction of the magnetic field? Explain. (1 marks)
3. Suppose instead of a proton, an electron entered the field moving the same direction (rightwards) and at the same speed as the proton. Identify two ways in which the electron’s trajectory would be different and explain. (2 marks)

               

2. At a given instant, a charge with q = -3.20 x

   

   10            C and m = 1.72 x 10^-27 kg moves along the x-axis when it encounters a uniform magnetic field given by the following: ?? = 2 ???+4 ??.? Right at this instant, it is found that the magnetic force on the charge is given by ? _? = 3.25 x 10^-14 N ??. Determine the charge’s speed and whether it is moving along the positive or negative x-axis. (Hint: start by letting

   

   ). (3 marks)  

 

3. A discus thrower starts from rest and, at t = 0 s, begins to spin, keeping the discus a constant distance of r = 0.65 m from the axis of rotation (that runs through the centre of their body). The thrower and discus undergo an angular acceleration given by the following function:

 

 

 

and at t = 1.5 s, releases the discus.

 

1. Through how many revolutions does the thrower turn before releasing the discus? (3 marks)

  

2. With what speed (in m/s) is the discus released? You can treat the discus as if it were a point mass for the purpose of this calculation.  (2 marks)

               

4. A model of a ceiling fan has been built out of tinker toys and set to rotate so that the axis of rotation is through the

 

1. Determine the moment of inertia of the combined shape, showing your work in detail. You can consider the central cylinder to be completely solid and imagine that the smaller rods are glued on right at the outer edge of the cylinder.  (3 marks)

  

Q4 Continued… NOTE: If you could not determine a value for part a, make an assumption about what you might have gotten and continue on to the remaining parts.

 

2. The fan is then mounted about a socket in the ceiling that allows it to rotate. String is spooled around the vertical rod as shown. The string is pulled with a constant force of 2.5 N and there is a frictional torque having a magnitude of 7 x 10^-3 N

   

   m. Determine the angular acceleration of the fan. (2 marks)

 

3. A total length of 15 cm of string is wrapped around the rod. If the fan experiences the same constant angular acceleration as in b) while the string unspools, determine its final angular velocity. (2 marks)

 

4. What is the fan’s final rotational kinetic energy? How much work does the string do on the fan? (2 marks)

               

5.  A holiday lantern with a mass of 25.0 kg is suspended at the end of a uniform rod with a mass of 10.0 kg that is hinged to a pole. The rod is supported by a cable attached at the end of the rod.

1. Determine the value of the tension in the cable. (3 marks)  
2. The hinge exerts a force on the rod that has both horizontal and vertical components. Determine the magnitude and direction of the hinge force. (3 marks)

  

6. You spin a bowling ball with a mass of 5.2 kg and a radius of 10.8 cm so that it spins about its axis on the smooth floor of the bowling alley with minimal friction. The bowling ball rotates 4 times per second. 

1. What is the bowling ball’s angular momentum? (2 marks)
2. Next, you drop a spherical wad of sticky clay onto the bowling ball so that it becomes stuck to the ball as shown. The clay has a mass of 1.40 kg and a radius of 4.4 cm. How many revolutions per second does the combined mass make? (3 marks)