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

Author Message
pnwokolo

Joined: 11 Mar 2010
Posts: 11
Location: Toledo,OH

 Posted: Thu Mar 11, 2010 4:39 pm    Post subject: Calculus-based physics-Please 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.
hepcj

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.
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 All times are GMT Page 1 of 1

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