of 14 7) For the two carts shown below, which of the following statements is te?
ID: 1714242 • Letter: O
Question
of 14 7) For the two carts shown below, which of the following statements is te? Assume steady flow and that the pipe diameter is uniform and equal for both carts 45° 45 Cart A Cart B Both carts move at the same speed, but Cart A moves to the right while Cant B moves to the left. (a) (b) Both carts move at the same speed, but Cart A moves to the left while Cart B moves to the (e) Both carts move to the right at the same speed. (d) Both carts move to the right bt Cart B moves faster than Cart A. ightExplanation / Answer
Problem 7,
(b) Both carts move at the same speed, but cart A moves to left, while cart B moves to the right.
This can be understood if we apply Newton's law of force in the x-direction. Let F is the force applied by the cart of the fluid, so that the velocity is changed in the x-direction, such that,
F = Rate of change of momentum = m2v2-m1v1, where m1 and m2 are the rate of mass flow, and v1 and v2 are the initial and final velocities in the x-direction.
in case of cart A, v1 is zero, while v2 has some value, therefore F becomes +ve, i.e. cart applies a force to the fluid in the +ve x-direction. Now according to the Newton's 3rd law, same force must be applied by the fluid on the cart, so the force on the cart is also F, but in -ve x-direction, so cart will move to the left. On the other hand for cart B, the initial velocity v1 has value, while v2 is zero. Due to the same magnitude of V and direction with vertical, the magnitude of F is same, but with -ve sign, so the direction becomes opposite, i.e. cart B moves to the right.
Due to the same magnitude of F, the magnitude of velocity and acceleration of the cart will be same, because both carts have same mass.
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