Question

You are driving on a mountain highway in your car, which is sloped downward at an angle of 7 degrees below the horizontal. Your car has a mass of 1200kg and your speed is 25 m/s. A moose steps out into the highway and you slam on your brakes, skidding to a stop. The force of kinetic friction between your car and the road is 9500.0 N.

a) Using an energy analysis, compute how far you skid before you come to a stop.

b) Using a force analysis, compute how far you skid before you come to a stop.

Answer 1

a)
let d is the distance travelled before coming to stop.

Apply net workdone = change in kinetic energy

W_gravity + W_friction = (1/2)*m*(vf^2 - vi^2)

m*g*sin(7)*d - 9500*d = (1/2)*1200*(0^2 - 25^2)

(1200*9.8*sin(7) - 9500)*d = -600*25^2

d = -600*25^2/(1200*9.8*sin(7) - 9500)

= 46.5 m <<<<<<<<<<<------------------Answer

b) Fnet = m*g*sin(7) - fk

m*a = m*g*sin(7) - fk

a = (m*g*sin(7) - fk)/m

= (1200*9.8*sin(7) - 9500)/1200

= -6.72 m/s^2

distance travelled before coming to stop,

d = (vf^2 -vi^2)/(2*a)

= (0^2 - 25^2)/(2*(-6.72))

= 46.5 m <<<<<<<<<<<<<<<--------------------Answer