It's possible you might be thinking of "Noise Level" by Raymond F. Jones as per Government investigating home library of missing inventor. To quote that answer:
Many of the country's top physicists are gathered together and are shown film of the inventor hovering using some sort of small anti-gravity device. They are told that, unfortunately, he shortly after died in a crash and is unit was completely destroyed. The government scientists can't make sense of the records he left behind, so they are asked to figure out what he did.
His lab is filled with odd stuff -- some high tech, some assorted, plus books on physics as well as the occult. A real mishmash.
The scientists persevere and, knowing the antigravity is possible, eventually come up with a huge, clumsy device that nevertheless hovers. They are then introduced to the (live) inventor -- who turns out to be an actor. They are told that this was an experiment to see if they could achieve more if they were forced to think outside the box.
It was first published in Astounding Science Fiction, December 1952 and has been widely reprinted: http://www.isfdb.org/cgi-bin/title.cgi?55972
And an excerpt from Scientists shown a fake anti-gravity device to motivate them to build the real thing:
… Dunning rose in a rather steep arc and levelled off.
Against the background,
he seemed about as high as the roof of the hangar beyond.
For about a hundred feet he drifted slowly, then accelerated his pace. …
Abruptly the screen flared.
A puff of light exploded from the pack on Dunning’s back.
For a terrible moment he seemed suspended in an attitude of violent agony.
Then he plunged like a dropped stone.
‘The remains of the device are here for your examination.
So far, we see only burned and bloody wreckage in it.
‘Dunning’s quite evident paranoia was carried out in an utter lack of notes. …
… We have to duplicate that work of Dunning’s.