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~christina~
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[SOLVED] Painting a Dome with rollerskates
Two prolific painters concoct a hair brain scheme for painting a spherical shaped
observatory dome. One painter has invented a pair of roller skates that will eject paint
only when the wheels of the skates are in contact with a surface. The daredevil of the
two, wearing the roller skates, starts with negligible velocity at the top of the dome and
coasts down over the dome's surface as shown in the figure below. As long as the
wheels are in contact, that surface of the dome will receive a coat of paint. The more
sensible painter is positioned with a net some distance from the base of the observatory
to break the daredevil's fall. The mass of the painter, including the skates, is 80 kg and
the radius of the dome is 8 m. A test run is made to demonstrate how much of the dome
can be painted in one pass. Assume that the painter's mass is constant over this one
run. Neglect friction and air resistance.
(a) Describe in angles (relative to the vertical) the portion of the dome that the daredevil would paint and the portion that would remain unpainted.
ABSOLUTELY NO IDEA HOW I WOULD GET THIS (doesn't help since I need to find this to do the rest of the problem
(b) If the net is removed, what velocity would the painter have when he impacts the ground?
I think I would need to find the painter's velocity as he leaves the dome and then just use
the uniform acceleration equations (projectile motion)
but I would I assume need to find the painter's angle relative to the horizontal when he leaves the dome for that. Then I would find distance to the floor, time it takes to get to zero and then velocity at that time
(c) What impulse would the ground deliver to the painter in order to stop him?
Hm..would it be[tex] p_f= p_i thus I= \Delta p= p_f-p_i[/tex]
(d) A person can just survive a full body collision if the average force is less than 72,000 Newtons. If it takes the ground 0.05 seconds to stop the painter, is it likely he will survive the fall? Explanations must include physics principle(s).
since [tex]F_{av}= \Delta p/ \Delta t[/tex] I would use the previous found Impulse and then find out if the force is greater or less
(e). Where should the assistant place the net from the dome to break the daredevil's fall?
I would find the distance in the x direction based on the time it takes to get to zero thus the floor
http://img440.imageshack.us/img440/3397/weeefq5.th.png
stated above except I don't know about the first part..
I'm not sure how to approach the first part A and find that angle or how they want me to state . Please help me
mass of skater: 80kg
[tex] r_{dome}= 8m [/tex]
Homework Statement
Two prolific painters concoct a hair brain scheme for painting a spherical shaped
observatory dome. One painter has invented a pair of roller skates that will eject paint
only when the wheels of the skates are in contact with a surface. The daredevil of the
two, wearing the roller skates, starts with negligible velocity at the top of the dome and
coasts down over the dome's surface as shown in the figure below. As long as the
wheels are in contact, that surface of the dome will receive a coat of paint. The more
sensible painter is positioned with a net some distance from the base of the observatory
to break the daredevil's fall. The mass of the painter, including the skates, is 80 kg and
the radius of the dome is 8 m. A test run is made to demonstrate how much of the dome
can be painted in one pass. Assume that the painter's mass is constant over this one
run. Neglect friction and air resistance.
(a) Describe in angles (relative to the vertical) the portion of the dome that the daredevil would paint and the portion that would remain unpainted.
ABSOLUTELY NO IDEA HOW I WOULD GET THIS (doesn't help since I need to find this to do the rest of the problem
(b) If the net is removed, what velocity would the painter have when he impacts the ground?
I think I would need to find the painter's velocity as he leaves the dome and then just use
the uniform acceleration equations (projectile motion)
but I would I assume need to find the painter's angle relative to the horizontal when he leaves the dome for that. Then I would find distance to the floor, time it takes to get to zero and then velocity at that time
(c) What impulse would the ground deliver to the painter in order to stop him?
Hm..would it be[tex] p_f= p_i thus I= \Delta p= p_f-p_i[/tex]
(d) A person can just survive a full body collision if the average force is less than 72,000 Newtons. If it takes the ground 0.05 seconds to stop the painter, is it likely he will survive the fall? Explanations must include physics principle(s).
since [tex]F_{av}= \Delta p/ \Delta t[/tex] I would use the previous found Impulse and then find out if the force is greater or less
(e). Where should the assistant place the net from the dome to break the daredevil's fall?
I would find the distance in the x direction based on the time it takes to get to zero thus the floor
http://img440.imageshack.us/img440/3397/weeefq5.th.png
Homework Equations
stated above except I don't know about the first part..
The Attempt at a Solution
I'm not sure how to approach the first part A and find that angle or how they want me to state . Please help me
mass of skater: 80kg
[tex] r_{dome}= 8m [/tex]
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