An iron bar of mass, 0.6 kg, slides down a frictionless incline 0.38 m high. At the bottom of the incline it collides and sticks to a magnet of mass, 0.94 kg. What is the speed of the combined masses after collision.
speed at bottom = sqrt(2 g h)
= sqrt (2 * 9.81 * .38)
= 2.73 m/s
momentum before crash = .6*2.73 = 1.64 kg m/s
same momentum after of course
new mass = .6 + .94 = 1.54 kg
so
1.64 = 1.54 v
v = 1.06 m/s
To find the speed of the combined masses after the collision, we can use the principle of conservation of energy. The initial potential energy of the iron bar will be converted into the final kinetic energy of the combined masses.
First, let's calculate the potential energy of the iron bar at the top of the incline. The potential energy is given by the formula:
Potential Energy = mass * gravitational acceleration * height
where the mass is 0.6 kg, the gravitational acceleration is 9.8 m/s^2, and the height is 0.38 m.
Potential Energy = 0.6 kg * 9.8 m/s^2 * 0.38 m
Potential Energy = 2.232 Joules
Since there are no external forces acting on the system, this potential energy will be entirely converted into kinetic energy after the collision. Therefore, we can equate the potential energy to the kinetic energy of the combined masses after the collision.
Kinetic Energy = (1/2) * total mass * velocity^2
where the total mass is the sum of the masses of the iron bar and the magnet, and the velocity is what we need to solve for.
Let's substitute the values we know. The total mass is 0.6 kg + 0.94 kg = 1.54 kg.
2.232 Joules = (1/2) * 1.54 kg * velocity^2
Now, rearranging the equation to solve for velocity:
velocity^2 = (2 * 2.232 Joules) / 1.54 kg
velocity^2 = 2.887 Joules / 1.54 kg
velocity^2 ≈ 1.8766
Taking the square root of both sides of the equation:
velocity ≈ √1.8766
velocity ≈ 1.369 m/s
Therefore, the speed of the combined masses after the collision is approximately 1.369 m/s.