Science Physics Cart A has mass M and is released from rest at a height 2 H on a ramp making an angle 2 with the horizontal, as shown. Cart B has mass 2 M and is...

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Question Cart A has mass M and is released from rest at a height 2H on a ramp making an angle 2θ with the horizontal, as shown. Cart B has mass 2M and is released from rest at a height H on a ramp ... making an angle θ with the horizontal. The carts roll toward each other, have a head-on collision on the horizontal portion of the ramp, and stick together. The masses of the carts' wheels are negligible, as are any frictional or drag forces. Before the carts are released, how does the mechanical energy of the Cart A-Earth system compare to the mechanical energy of the Cart B-Earth system? Explain your answer. The mechanical energy of both are equal because the gravitational potential energy is equal to mgh. For cart A-earth system the gravitational potential energy is M2HG and for cart B-earth system it is 2MHG, which is equal therefore the mechanical energy of the Cart A-Earth system and the Cart B-Earth system are equal. When both carts reach the bottom of their respective ramps, how does the momentum of cart A compare to the momentum of cart B? Explain your answer. The momentum of cart B is greater than the momentum of cart A. Since the gravitational potential energy is the same and it becomes kinetic energy, then their velocities are the same. However, the equation for linear momentum is m*v and cart B has a mass of 2M and cart A has a mass of M. Since they have the same velocities, but cart B has a greater mass than cart A, cart B will have a greater momentum than cart A. Indicate whether the carts remain at rest, move to the left, or move to the right after the collision. Explain how you arrived at your answer. The carts will move the left after the collision. If both carts have the same velocity, but cart B has a greater momentum than we can do conservation of momentum with them sticking together. Since cart A is moving right we can consider that the positive direction. Since cart B is moving left, we can consider the left the negative direction. Let V be the velocity for both carts. Since cart A has a momentum of M*V and cart B has a momentum 2M*(-V) which (when put into the equation for a sticking collision of conservation of momentum) it is -M*V = (3M)V(prime) which then makes the velocity or V(prime) after the collision (-V/3). Since we designated the left direction to be negative then the cart will move to the left after the collision. 1. Consider the time interval from when the two carts are released until just after they collide. i. For the system consisting of the two carts and Earth, indicate whether the total mechanical energy increases, decreases, or remains the same. Justify your answer. The total mechanical energy remains the same. The two carts stick together meaning they are perfectly inelastic. This would mean that the amount of energy loss in the collision would be converted into heat. This would mean that the two carts and Earth would remain constant which would mean that the two carts and the Earth would have the same energy. ii. For the system consisting of only the two carts, indicate whether the total mechanical energy increases, decreases, or remains the same. Justify your answer. The total mechanical energy decreases because in this time interval there is a decrease in mechanical energy due to friction and a piece of the total energy in the system of the two cars is converted into heat energy therefore the total mechanical energy decreases. These are all my answers, can YOU CHECK THEM (I WILL NOT COPY YOUR ANSWER), but I am confused about B and the last questions. Can you please help. Thank you. [Show More]

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