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rustyshackle
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Ok, first time posting...hopefully I do this correctly, as I have found myself in a bind on this one. It is a question comparing the mechanical energy of two masses falling in different ways in which you are given the option of greater than, less than, or equal to.
The figure below (In the attachment) shows two blocks, m1 and m2 of the same mass. Block 1 starts from rest and slides down a frictionless incline from a height H from the floor while block 2 is dropped from rest at the same time from the same height.At height h block 1 falls off the incline.
1) The velocity of block 1 when it is at height h is (greater than/less than/equal to) the velocity of block2 when it is also at height h.
2) The kinetic energy of block 2 when it is at height his (greater than/less than/equal to) the kinetic energy of block 1 when it is also at height h.
3) The change in potential energy of block 1 when it slides from H to h is (greater than/less than/equal to) the change in potential energy of block 2 when it falls from H to h.
4) The time it takes for block 1 to fall from h to the floor is (greater than/less than/equal to) the time it takes block 2 to fall from h to the floor.
5) The time it takes for block 2 to fall from H to h is (greater than/less than/equal to) the time it takes to slide the same vertical distance.
PE = mgh
KE = .5mv^2
v= sqrt(2gh)
My attempts so far I have been incorrect, but here is what I thought it was and why:
1) Equal to. Because both have the same change in potential energy and by energy conservation principle will have the same kinetic energy at the bottom of the slide
when there is no friction. Both will have speed v = sqrt(2gh)
2) Equal to. Both have the same height at h and therefore have equal PE, meaning equal PE.
3) Equal to. While the change is more sudden in mass two, both are undergoing the same change in PE from H to h.
4) Equal to. Once they reach point h, they have the same speed and same height, and therefore reach it at the same time.
5) Greater than. Mass 2 has a more sudden change in PE and there gets up to speed faster than mass 1.
Any help on this would be greatly appreciated, as I have referenced the internet, my textbook, and lecture notes and have still not found any help. Thank you.
Homework Statement
The figure below (In the attachment) shows two blocks, m1 and m2 of the same mass. Block 1 starts from rest and slides down a frictionless incline from a height H from the floor while block 2 is dropped from rest at the same time from the same height.At height h block 1 falls off the incline.
1) The velocity of block 1 when it is at height h is (greater than/less than/equal to) the velocity of block2 when it is also at height h.
2) The kinetic energy of block 2 when it is at height his (greater than/less than/equal to) the kinetic energy of block 1 when it is also at height h.
3) The change in potential energy of block 1 when it slides from H to h is (greater than/less than/equal to) the change in potential energy of block 2 when it falls from H to h.
4) The time it takes for block 1 to fall from h to the floor is (greater than/less than/equal to) the time it takes block 2 to fall from h to the floor.
5) The time it takes for block 2 to fall from H to h is (greater than/less than/equal to) the time it takes to slide the same vertical distance.
Homework Equations
PE = mgh
KE = .5mv^2
v= sqrt(2gh)
The Attempt at a Solution
My attempts so far I have been incorrect, but here is what I thought it was and why:
1) Equal to. Because both have the same change in potential energy and by energy conservation principle will have the same kinetic energy at the bottom of the slide
when there is no friction. Both will have speed v = sqrt(2gh)
2) Equal to. Both have the same height at h and therefore have equal PE, meaning equal PE.
3) Equal to. While the change is more sudden in mass two, both are undergoing the same change in PE from H to h.
4) Equal to. Once they reach point h, they have the same speed and same height, and therefore reach it at the same time.
5) Greater than. Mass 2 has a more sudden change in PE and there gets up to speed faster than mass 1.
Any help on this would be greatly appreciated, as I have referenced the internet, my textbook, and lecture notes and have still not found any help. Thank you.
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