A 10 kg cart is moving along an air track with an initial velocity of 6 m/s. A s
ID: 1553785 • Letter: A
Question
A 10 kg cart is moving along an air track with an initial velocity of 6 m/s. A second 16 kg cart is moving in the opposite direction with a speed of 8 m/s. What is the velocity of both carts after they collide? Assume the collision is completely elastic. A rocket in space is travelling at an initial speed of 120 m/s. After burning some fuel its speed increased to 580 m/s. If the exhaust speed of the fuel is 1800 m/s relative to the rocket, what percentage of the initial mass is lost? A force in the x direction is applied to a 6 kg box that is sitting on a horizontal, frictionless surface. The force varies with position as F(x) = 18 - 0.6x^2. If the box starts off at rest and is at an initial position of x = 0, what is the speed of the box after travelling 8 m? A 10 kg mass initially has a momentum vector p = 30i + 40j while a 25 kg mass initially has a momentum vector p = -160i - 95j. After a collision between the two masses the 25 kg mass now has a momentum vector p = -150i - 20j. Using momentum conservation, prove whether this is a completely elastic, inelastic or completely inelastic collision. What is the angle between the vector A = with the negative z axis? A 50 kg crate is being lowered down a ramp by a rope that acts parallel to the surface of the ramp. The rope is being used to slow the acceleration and acts up the ramp. During an 8 m path along the ramp, the crate constantly accelerates from 2 m/s to 6 m/s. The ramp makes an angle of 30 with the horizontal and has a coefficient of kinetic friction between it and the crate of mu_k = 0.24. What is the work done by each force (gravity, tension, normal and friction) during 8 m displacement? This problem will use the graph of position at the bottom left of this page for both parts (Assume that gravity acting in the -y direction as normal and no other forces (other than normal force) are acting on the system). For clarity, Path 1 and Path 2 are identical until the x = 4 m position where Path 2 moves down. Assume that the sharp edges are smooth curves. (a): Two identical objects are released at the same time at the x = 0 m position. One object is on Path 1 and the on Path 2. Assuming mechanical energy is conserved, which ball will reach the x = 10 m position first? Your options Path 1, Path 2, Same Time. (b): Assume mechanical energy is conserved, indicate whether the following are positive, negative or zero. Please indicate all answers on your answer sheet. Subscripts indicate the path number in question. KE_1(x = 4) - KE_1(x = 2) U_2(x = 10) - U_2(x = 7) U_2(x = 8) - U_1(x = 8) KE_2(x = 8) - KE_1(x = 8)Explanation / Answer
by conservation of momentum
initial momentum = final momentum
momentum = mass * velocity
initial momentum = 10 * 6 - 16 * 8
final momentum = 10 * v1 + 16 * v2
so,
10 * 6 - 16 * 8 = 10 * v1 + 16 * v2 --------------(1)
by conservation of energy
initial energy = final energy
energy = 0.5 * mass * velocity^2
initial energy = 0.5 * 10 * 6^2 + 0.5 * 16 * 8^2
final energy = 0.5 * 10 * v1^2 + 0.5 * 16 * v2^2
so,
0.5 * 10 * 6^2 + 0.5 * 16 * 8^2 = 0.5 * 10 * v1^2 + 0.5 * 16 * v2^2 -----------------(2)
on solving equation 1 and 2 we'll get
speed of 10 kg cart v1 = -11.2308 m/s
speed of 16 kg cart v2 = 2.7692 m/s
-ve sign indicate speed in opposite direction
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