Student question: #13-#16. In order to find the potential energy, do I have to calculate the energy only among consecutive charges, or do I have to calculate the energy for charges that are diagonally opposite each other as well?
Dr. Winters' answer: To find the total potential energy of the system you need to include the potential energy between all pairs of charges.
Good luck.
Sunday, February 5, 2012
Sunday, January 29, 2012
HW15 #2
This question asks for the electric flux. It should ask for the answer in units of (N*m^2)/C, but it incorrectly asks for the answer in units of N/C.
Sunday, November 20, 2011
HW9 slippage
Student question: A few questions in the homework refer to a point in which objects move without slippage. I know this means that it is rolling, but I don't know what equations need to be satisfied for this to occur.
Dr. Winters' response: Things slide when there is no friction. Things move without slippage when there is friction. So if a problem says that an object moves or rolls without slipping then it means that you need to consider the force due to friction. And you need to consider the force of friction when you are looking at torques, because the force of friction acts on the outside surface of a wheel or ball, and that is a distance r from the center of mass (so there is torque τ=rF (the angle between friction, which acts tangent to the surface, and the radius r is 90 degrees so sinθ=1). It is probably a torque problem.
Hope that helps. Good luck.
Dr. Winters' response: Things slide when there is no friction. Things move without slippage when there is friction. So if a problem says that an object moves or rolls without slipping then it means that you need to consider the force due to friction. And you need to consider the force of friction when you are looking at torques, because the force of friction acts on the outside surface of a wheel or ball, and that is a distance r from the center of mass (so there is torque τ=rF (the angle between friction, which acts tangent to the surface, and the radius r is 90 degrees so sinθ=1). It is probably a torque problem.
Hope that helps. Good luck.
Saturday, November 19, 2011
HW9 #4
I'm really stuck on this problem... I know how to find the instantaneous angular velocity and the average angular acceleration, but I don't know how to calculate the instantaneous angular acceleration. I tried a few different methods, but none of them are right. For example, I tried alpha = (v^2)/(r^2), since a = alpha*r and in this case, the acceleration is centripetal acceleration. Did anyone figure out how to do this one?
Saturday, November 12, 2011
HW8 #8
Is this question referring to the initial speed of the point or after the time interval given in #5?
HW8 #10
I seem to be stuck on this problem. I converted the rotational velocity so that the units would be rad/s instead of rev/min. I calculated the radius (in m) using the diameter (given in m). I plugged these values into the KE =(1/2)(m)(wr)^2 equation [w = lower case omega], but my answer was incorrect. What am I doing wrong?
Sunday, November 6, 2011
HW7 #7
Student question:
I tried to do #7, but it doesn't seem to work. I have the following values given:
A projectile of mass 5 kg is fired with an initial speed of 198 m/s at an angle of 25◦ with the horizontal. At the top of its trajectory, the projectile explodes into two fragments of masses 3.2 kg and 1.8 kg . The 1.8 kg fragment lands on the ground directly below the point of explosion 2.8 s after the explosion.
The acceleration due to gravity is 9.81 m/s2 .
Find the magnitude of the velocity of the 3.2 kg fragment immediatedly after the explosion.
I know that the 1.8 kg has no horizontal velocity because it falls straight down, so I found the horizontal velocity of the 3.2 kg fragment by doing (5 kg)(198cos25 m/s)/(3.2 kg). I tried to find the vertical velocity by finding the initial vertical velocity of the 1.8 kg. I used X=V0t+1/2at^2 and used conservation of energy in the vertical direction to find the height, or X. I then put this velocity into conservation of momentum in the vertical direction and found the vertical velocity for the 3.2 kg fragment. Finally, I used the pythagorean triangle to find the resulting velocity. I've done this five times and it hasn't worked. Am I doing something wrong or missing some important step? If you could reply as soon as possible, I'd greatly appreciate it. Thanks!
Dr. Winters' response:
Very nice start. This is a fairly complex problem, where you need to look at kinematics and momentum. I like the way you found the horizontal component of the 3.2kg fragment using conservation of momentum in the horizontal direction.
I didn't follow how you found the vertical velocity of the 1.8kg fragment. It sounds as though you first found the vertical velocity and then found the height. I think that's backwards. You can find the height using kinematics (the explosion takes place at the top of the trajectory). Knowing the height and the time to fall, you can find the initial vertical velocity of the 1.8kg fragment.
After that, use conservation of momentum in the vertical direction, as you described, to find the vertical component of velocity of the 3.2kg fragment.
It sounds as though you are doing everything right except attacking the middle calculation backwards. Hope that helps. Good luck.
I tried to do #7, but it doesn't seem to work. I have the following values given:
A projectile of mass 5 kg is fired with an initial speed of 198 m/s at an angle of 25◦ with the horizontal. At the top of its trajectory, the projectile explodes into two fragments of masses 3.2 kg and 1.8 kg . The 1.8 kg fragment lands on the ground directly below the point of explosion 2.8 s after the explosion.
The acceleration due to gravity is 9.81 m/s2 .
Find the magnitude of the velocity of the 3.2 kg fragment immediatedly after the explosion.
I know that the 1.8 kg has no horizontal velocity because it falls straight down, so I found the horizontal velocity of the 3.2 kg fragment by doing (5 kg)(198cos25 m/s)/(3.2 kg). I tried to find the vertical velocity by finding the initial vertical velocity of the 1.8 kg. I used X=V0t+1/2at^2 and used conservation of energy in the vertical direction to find the height, or X. I then put this velocity into conservation of momentum in the vertical direction and found the vertical velocity for the 3.2 kg fragment. Finally, I used the pythagorean triangle to find the resulting velocity. I've done this five times and it hasn't worked. Am I doing something wrong or missing some important step? If you could reply as soon as possible, I'd greatly appreciate it. Thanks!
Dr. Winters' response:
Very nice start. This is a fairly complex problem, where you need to look at kinematics and momentum. I like the way you found the horizontal component of the 3.2kg fragment using conservation of momentum in the horizontal direction.
I didn't follow how you found the vertical velocity of the 1.8kg fragment. It sounds as though you first found the vertical velocity and then found the height. I think that's backwards. You can find the height using kinematics (the explosion takes place at the top of the trajectory). Knowing the height and the time to fall, you can find the initial vertical velocity of the 1.8kg fragment.
After that, use conservation of momentum in the vertical direction, as you described, to find the vertical component of velocity of the 3.2kg fragment.
It sounds as though you are doing everything right except attacking the middle calculation backwards. Hope that helps. Good luck.
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