One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal, frictionless tabletop, which is a distance above the floor. A block of mass M is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance x, as shown above. The block is released, follows the trajectory shown, and strikes the floor a horizontal distance D from the edge of the table. Air resistance is negligible.
Determine expressions for the following quantities in terms of M,x, D,h, and g. Note that these symbols do not include the spring constant.
(a) The time elapsed from the instant the block leaves the table to the instant it strikes the floor
(b) The horizontal component of the velocity of the block just before it hits the floor
(c) The work done on the block by the spring
(d) The spring constant
One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal, frictionless tabletop, which is a distance above the floor. A block of mass M is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance x, as shown above. The block is released, follows the trajectory shown, and strikes the floor a horizontal distance D from the edge of the table. Air resistance is negligible.
Determine expressions for the following quantities in terms of M,x, D,h, and g. Note that these symbols do not include the spring constant.
(a) The time elapsed from the instant the block leaves the table to the instant it strikes the floor
(b) The horizontal component of the velocity of the block just before it hits the floor
(c) The work done on the block by the spring
(d) The spring constant
