Mass m moves to the right with speed =v along a frictionless horizontal surface and crashes into an equal mass m initially at re
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Ok, a couple of things have to be accounted for here. First, since the block is moving relative to the wall we have to use the kinetic coefficient of friction, 0.40. The second consideration is that since the block is moving at a constant velocity, the acceleration is zero. This means, by Newton's second Law, that the net force is zero. So the force of gravity must be equal to the friction force of the wall resisting its fall. This friction force is the product of the normal force (which we are seeking) and the kinetic coefficient of friction. We can then set these two forces equal:
If we neglect frictional force, the total mechanical energy of the ball is conserved.
The total mechanical energy of the ball is the sum of its kinetic energy K and its potential energy U:
where the kinetic energy depends on the speed v of the ball:
while the potential energy depends on the height h at which the ball is:
As the ball travels along the roller coaster, there is a continuous conversion between kinetic and potential energy, because the total mechanical energy E has always the same value. Therefore, when the ball goes on top of a hill, its height h increases and its potential energy U increases as well, while the speed v decreases and K decreases. Vice-versa, when the ball reaches the bottom of a hill, its height h decreases and therefore the potential energy U decreases, while the speed v increases and therefore the kinetic energy K of the ball increases as well.
The total mechanical energy of the ball is the sum of its kinetic energy K and its potential energy U:
where the kinetic energy depends on the speed v of the ball:
while the potential energy depends on the height h at which the ball is:
As the ball travels along the roller coaster, there is a continuous conversion between kinetic and potential energy, because the total mechanical energy E has always the same value. Therefore, when the ball goes on top of a hill, its height h increases and its potential energy U increases as well, while the speed v decreases and K decreases. Vice-versa, when the ball reaches the bottom of a hill, its height h decreases and therefore the potential energy U decreases, while the speed v increases and therefore the kinetic energy K of the ball increases as well.