particle 1 of mass m1 = 0.29 kg slides rightward along an x axis on a frictionless floor with a speed of 1.8 m/s. When it reaches x = 0, it undergoes a one-dimensional elastic collision with stationary particle 2 of mass m2 = 0.40 kg. When particle 2 then reaches a wall at xw = 70 cm, it bounces from it with no loss of speed. At what position on the x axis does particle 2 then collide with particle 1?
The first collision (conservation of energy, momentum) gives you the speeds of M1 and m2 after the collision. Then, the distance m2 travels is 70 cm + (70-x) cm. But it does it in the same time as m1 travel x cm. You have the distances, velocitys, and times, solve for x.
ok so velocity of m1 = 150 m/s and m2 = -29 m/s.....where do i go from there?
Okay, dude your velocities are ridiculous, does 150 m/s even make ANY sense to you?
From the given information, the velocity of particle 1 (m1) after the collision is 150 m/s to the right, and the velocity of particle 2 (m2) after the collision is -29 m/s to the left.
To find the position on the x-axis where particle 2 collides with particle 1, we can use the fact that the distance traveled by each particle is equal when they collide.
The distance traveled by particle 1 (m1) can be calculated by multiplying its velocity (150 m/s) by the time it takes to reach the collision point.
The distance traveled by particle 2 (m2) can be calculated by adding the initial distance from the wall (70 cm) to the distance it travels after the collision, which is given by (70 - x), where x is the distance from the collision point to the wall.
Since both particles travel the same time to reach the collision point, their distances must be equal. Therefore, we can set up the equation as:
distance m1 = distance m2
Using the formula for distance (distance = velocity * time), we can write the equation as:
150 * t = -29 * t
where t is the time taken for both particles to reach the collision point.
Now, we need to solve this equation to find the value of t. Dividing both sides of the equation by t, we get:
150 = -29
This is a contradiction since 150 is positive, and -29 is negative. Therefore, there is no solution for this equation, which means that particle 2 (m2) does not collide with particle 1.
Hence, particle 2 will not collide with particle 1 on the x-axis in this scenario.