
Splung.com Physics Forum Discuss physics or ask questions. Part of the Splung.com physics web site.

View previous topic :: View next topic 
Author 
Message 
pnwokolo
Joined: 11 Mar 2010 Posts: 11 Location: Toledo,OH

Posted: Thu Mar 11, 2010 4:39 pm Post subject: Calculusbased physicsPlease help solve this problem! 


Two fan carts labeled A and B are placed on opposite sides of a table with their fans
pointed in the same direction, as shown. Cart A is weighted with iron bars so it
is twice as heavy as cart B. When the fans are turned on, they provide a constant
force on the cart independent of its mass. Assume that friction is small enough to be
neglected. The fans are set with a time so that after they are switched on, they stay
on for a fixed length of time, t, and then go off.
(a) Just after the fans go off, which of the following statements are true about the
momenta of the two carts?
i. pA > pB
ii. pA = pB
iii. pA < pB
(b) Just after the fans go off, which of the following statements is true about the
kinetic energies of the two carts?
i. KA > KB
ii. KA = KB
iii. KA < KB
(c) Which of the following statements is true? You may choose as many as you like,
or none. If you choose none, specify this.
i. After the fan is turned on, each cart moves at a constant velocity, but the
two velocities are different from each other.
ii. The kinetic energy of each cart is conserved.
iii. The momentum of each cart is conserved. 

Back to top 


hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Fri Mar 12, 2010 1:55 pm Post subject: 


This problem is to do with Netwon's laws of motion. Essentially, the only difference between the carts is the mass, cart B has twice the mass of cart A.
a) We know from Netwon's 2nd law, F= ma is the same as F = dp/dt
Since the force is the same for both carts the momentum will be the same.
b) The velocities will be different as cart B is twice the mass so the velocity will be half that of cart A.
The kinetic energy of the cart is given by
KE = (1/2) m v^2
since the velocity of cart A is twice that of cart B
KE_A =0.5 m (2v)^2 = 2mv^2
KE_B =0.5 * (2m) v^2 = mv^2
or cart A has twice the KE of cart B.
c) While the fan is switched on, there is a force applied to each cart which will cause it to accelerate. Therefore i) is false, ii) is false because the KE depends on the square of velocity.
iii) is true since F= dp/dt and it is the same force applied to both carts. 

Back to top 




You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum

© Copyright 2010 Splung.com
