2. A block of mass m is moving with speed v along a horizontal surface when it collides with a uniform rod of mass 2m and length L attached at one end to a pivot. The surface and pivot have negligible friction. The rod is vertical when the block collides with the end of the rod. The block sticks to the rod, and the block-rod system rotates so that the end of the rod reaches a height h, as shown above. The total rotational inertia of the rod about the pivot is 2mL'/3. Express answers in parts (a), (b), and (c) in terms of m, L., v, and physical constants as appropriate. 2m, L a. Derive an expression for the angular speed of the block-rod system immediately after the collision. Show that the nge in height h of the bottom of the rod can be given by the equation A= 3v²/20g . c. Derive an expression for the mechanical energy dissipated during the collision.
2. A block of mass m is moving with speed v along a horizontal surface when it collides with a uniform rod of mass 2m and length L attached at one end to a pivot. The surface and pivot have negligible friction. The rod is vertical when the block collides with the end of the rod. The block sticks to the rod, and the block-rod system rotates so that the end of the rod reaches a height h, as shown above. The total rotational inertia of the rod about the pivot is 2mL'/3. Express answers in parts (a), (b), and (c) in terms of m, L., v, and physical constants as appropriate. 2m, L a. Derive an expression for the angular speed of the block-rod system immediately after the collision. Show that the nge in height h of the bottom of the rod can be given by the equation A= 3v²/20g . c. Derive an expression for the mechanical energy dissipated during the collision.
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Transcribed Image Text:2. A block of mass m is moving with speed v along a horizontal surface when it collides
with a uniform rod of mass 2m and length L attached at one end to a pivot. The surface
and pivot have negligible friction. The rod is vertical when the block collides with the end
of the rod. The block sticks to the rod, and the block-rod system rotates so that the end
of the rod reaches a height h, as shown above. The total rotational inertia of the rod
about the pivot is 2mL/3. Express answers in parts (a), (b), and (c) in terms of m, L, v,
and physical constants as appropriate.
2m, L
a. Derive an expression for the angular speed of the block-rod system immediately
after the collision.
b. Show that the change in height h of the bottom of the rod can be given by the
equation A = 3v-/20g.
c. Derive an expression for the mechanical energy dissipated during the collision.
Transcribed Image Text:d. Students use the setup to determine an experimental value for the acceleration
due to gravity g. The students use a block of mass 500g and a rod of mass 1.0
kg and length 1.0m. For each trial, the rod is set in its vertical position, and the
block is launched toward it. The speed of the block is varied for each trial, and
the height is measured. The data are shown in the chart below.
v(m/s)
1.5
2
2.5
3
h(m)
0.015
0.034
0.060
0.096
0.138
Which quantities should be graphed on the vertical and horizontal axes to yield a
straight line whose slope could be used to calculate a numerical value for the acceleration due
to gravity g? Use the remaining rows in the table above, as needed, to record any quantities
that you indicated that are not given.
e. Plot the experimental data for the quantities indicated in part on the graph below.
Clearly scale and label all axes including units, if appropriate. Draw a straight line
that best represents the data.
1 Using your straight line, determine an experimental value for g.
g. A new block of mass m is used. This block is made of a material that makes an
elastic collision with the rod when the block and rod collide. WilIl the height h
increase, decrease, or stay the same?
Increase
Justify your answer.
Decrease
Stay the same
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