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Once the FSR is pressed the output of the comparator should go high. Since there is not really any "delicate" logic behind this schematic I was wondering if a pull-up resistor is really necessary for this application that involves simply turning ON a DC motor while the FSR is pressed. The comparators' data sheet does say that a pull-up is recommended. What do you guys think?

Comparators Data Sheet: https://www.onsemi.com/pub/Collateral/NCS2250-D.PDF

FSR switch cirucit

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    \$\begingroup\$ A lot of comparators have open collector outputs and thus need the pullup. A quick scan of your datasheet link suggests the 2252 is open collector but the 2250 has a totem pole output. So using the 2250 you don't need the pullup, but with the 2252 you do, \$\endgroup\$ – user_1818839 May 18 '20 at 18:11
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The second paragraph of the datasheet you linked says:

These single channel devices are available with a complementary push−pull output in the NCS2250 or with an open drain output in the NCS2252.

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Table 2 confirms that you don't need one for the 2250. The push-pull output can pull the output high or low without the need for a pull-up. The 2252 can only pull low so it does one. The open-drain type can be convenient when several can be wired in parallel to provide an OR function; any one of them pulling low pulls the output low.

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