It is extremely common, and is caused by friction between the penis and the vaginal opening. This means there is too little lubrication, which is easily corrected by the use of some kind of lubricant - saliva or even better, water or silicon based lube. Water base is essential if a latex condom is used, since latex does not tolerate oils or greases.
The fact that there is too little lubrication is nothing to be ashamed of. Some women just become wetter than others. Also, the amount of foreplay
greatly affects the amount of natural lubricants in the vagina. The more turned on a woman is, the more her body produces fluids for easy penetration.
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The question is not, why does it burn during sex, the question is referring to "when the penis first enters the vagina". This could be caused by the female having a yeast infection due to the increase in acidity. this could also leave the male slightly itchy afterwards, not necessarily like jock itch but along the length of the penis.
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Friction during entry of the penis can be caused by a lack of lubrication as noted in the first response. Another cause can be muscle tension. If the female is tense or not receptive then her vaginal muscle will be tense also. In some instances the tension can be so great as to resist penetration by the penis, causing pain to both partners, as a burning or bruising sensation. The use of synthetic and natural lubricants during foreplay aid in the relaxation of the vagina. If foreplay is performed long enough to cause the secretion of natural lubricants from specialized glands near the vaginal opening then the vaginal wall is not likely to be as tense and friction will be reduced to a pleasurable level. Lubricated condoms are available to minimize the friction burn during entry if natural secretions are insufficient.
The second answer has some value as well. A yeast infection in the female can cause a 'burn' sensation during penile entry and in some cases the male who contracts a serious yeast infection from his infected partner may have the similar symptoms. Usually signs of yeast infection are less obvious in the male than in the female. Going back to the idea of muscle tension, if a woman is aware she has something wrong , say a yeast infection, and she has not told her partner, it's possible she might be less relaxed than usual, and less receptive on a subconscious level.