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"an object of mass 1kg falls a distance of 5m onto a horizontal surface and rebounds to a vertical height of 2m calculate the change in momentum"
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To calculate the change in momentum, we need to first calculate the initial momentum and final momentum of the object.
Initial momentum = mass x initial velocity
The object was initially at rest before it fell, so the initial velocity is 0. Therefore, initial momentum = 0.
Final momentum = mass x final velocity
To calculate the final velocity, we can use the principle of conservation of energy. The potential energy at the top of the rebound (when the object is at a height of 2m) is equal to the kinetic energy just before the rebound (when the object is at a height of 0m).
Potential energy at 2m = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical height (2m). Therefore, potential energy = 1kg x 9.8 m/s^2 x 2m = 19.6 J.
Kinetic energy just before the rebound = (1/2)mv^2, where m is the mass and v is the velocity. Since the object is falling from a height of 5m, we can use the equation for gravitational potential energy to find its velocity just before the rebound:
Potential energy at 5m = mgh
Kinetic energy just before the rebound = Potential energy at 5m
(1/2)mv^2 = mgh
v^2 = 2gh
v = sqrt(2gh)
v = sqrt(2 x 9.8 m/s^2 x 5m)
v = 9.90 m/s
Therefore, kinetic energy just before the rebound = (1/2) x 1kg x (9.90 m/s)^2 = 49.0 J.
Since kinetic energy is conserved in an elastic collision, the final kinetic energy just after the rebound will be equal to the initial kinetic energy just before the fall. Therefore, final velocity = sqrt(2 x 49.0 J / 1kg) = 9.90 m/s.
Final momentum = 1kg x 9.90 m/s = 9.90 kg m/s
Change in momentum = final momentum - initial momentum = 9.90 kg m/s - 0 = 9.90 kg m/s
Therefore, the change in momentum of the object is 9.90 kg m/s.