A truck accelrates with 5 metre per second square. a block of mass 4 kg is kept at the distance 6m from the rear end of the truck and the coefficient of friction between floor of the truck and block is 0.2. calculate the time taken by the block to fall from the truck.

Asked by Raja | 30th Aug, 2015, 05:27: PM

Expert Answer:

begin mathsize 12px style Given colon Mass space of space the space block comma space straight m space equals space 4 space kg acceleration space of space truck comma space straight a space equals space 5 space straight m divided by straight s squared distance space of space block space from space rear space end comma space straight s space equals space 6 space straight m space coefficient space of space friction comma space straight mu space equals space 0.2  Force space on space the space block space due space to space accelerated space motion space of space the space truck comma straight F space equals space ma space equals space 4 space cross times space 5 space equals space 20 space straight N This space force space straight F space is space in space the space forward space direction.  Let space straight F apostrophe space be space theNormal space Reaction space on space the space block space is space equal space to space the space straight F space in space the space backward space direction. Which space is space opposed space by space force space of space limiting space friction comma space straight f space equals space μR space equals space straight mu space cross times space mg space equals space 0.2 space cross times space 4 space cross times space 10 space equals space space 8 space straight N Therefore comma space the space net space force space on space block space in space the space backward space direction space is comma space space straight P space equals space straight F apostrophe space minus space straight f space equals space 20 space minus space 8 space equals space 12 space straight N Hence comma space backward space acceleration space produced space in space the space box comma space straight a space equals space straight P over straight m space equals space 12 over 4 space equals space 3 space straight m divided by straight s squared Let space straight t space be space the space time space taken space by space block space to space travel space straight a space distance space straight s space and space fall space from space the space truck comma space then straight s space equals space ut space plus space 1 half at squared 6 space equals space 0 space cross times space straight t space plus space 1 half space cross times space 3 space cross times space straight t squared 4 space equals space space straight t squared straight t space equals space 2 space straight s Hence comma space time space taken space by space the space block space to space fall space from space the space truck space is space 2 space straight s. end style

Answered by Priyanka Kumbhar | 31st Aug, 2015, 09:31: AM