# Rounded top hill question

## Homework Statement

a 1000kg sports car moving at 20m/s crosses the round top of a hill (radius of 100 m) . Determine the normal force on the car

## Homework Equations

Newton’s second law
F=ma

## The Attempt at a Solution

I figured out the centripetal acceleration
Ac= v^2/r
= 4 m/s^2
My attempt at finding the normal force :
Fn= mv^2/r + mg
= 1,000•20^2 / 100 + 1,000•9.8
=5800N
But the answer is 6206 N
Where did I go wrong ?

haruspex
Homework Helper
Gold Member
2020 Award
Fn= mv^2/r + mg
Presumably you are basing that on ΣF=ma. In that regard, what is ΣF and what is a? Pay attention to signs.
But maybe that was just a typo, since you have applied the correct sign to get this:
=5800N
I cannot explain 6206N.

lekh2003
Gold Member
Where did I go wrong ?

I honestly cannot make out what you have done wrong. Actually, I remember doing this exact question when I was studying. It was confusing, but you seem to have gotten it. 6206 N seems wrong. Forget about the numerical value, why would your physics textbook or class use 4 sig-figs for a problem with only 1 sig-fig.

Either you haven't given all the information (which I doubt) or, and I really don't want to jump to conclusions, the answer is wrong. Please ask you teacher or tutor and let us know what the answer or issue was.

P.S. Are you studying from CTY? All your posts seem to be questions from there. Just guessing, could be wrong.
{"ft_lang_label":"__label__en","ft_lang_prob":0.75857407,"math_prob":0.44420183,"size":436,"snap":"2021-31-2021-39","text_gpt3_token_len":154,"char_repetition_ratio":0.097222224,"word_repetition_ratio":0.0,"special_character_ratio":0.36926606,"punctuation_ratio":0.06185567,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9659566,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-19T15:03:08Z\",\"WARC-Record-ID\":\"<urn:uuid:d318a8a6-3756-4f5d-831b-9d850eb28dad>\",\"Content-Length\":\"69464\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f6e29a0c-5597-465b-8a35-85a96f39c077>\",\"WARC-Concurrent-To\":\"<urn:uuid:df2f5190-47f7-4517-970f-74c86a59f798>\",\"WARC-IP-Address\":\"172.67.68.135\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/rounded-top-hill-question.934369/\",\"WARC-Payload-Digest\":\"sha1:SC6LU443AYKGUB6OCL6NDLJS4B62XZN3\",\"WARC-Block-Digest\":\"sha1:QGYEK7BJGSX6NL7J7IMAUMRYCOJU6WWQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056890.28_warc_CC-MAIN-20210919125659-20210919155659-00287.warc.gz\"}"}