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2 years ago

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a 1200 kg trailer is hitched to a 1400 kg car. the car and trailer are traveling at 72 km.h when the driver applies the brakes o

n both the car and the trailer. knowing that the braking forces exerted on the car and the trailer are 5000 N and 4000 N respectively, determine (a) the distance traveled by the car and trailer before they come to a stop and (b) the horizontal component of the force exerted by the trailer hitch

1 answer:

Sergio [31]2 years ago

5 0

Answer:

a) 8.67m

b) 1000N

Explanation:

(a) To find the distance you use the second Newton Law for both car and trailer, in order to calculate the dis-acceleration of the system:

$F=ma\\\\a_=\frac{F}{m}=\frac{5000N+4000N}{1400kg+1200kg}=3.46\frac{m}{s^2}$

once you have this value, you use the the following kinematic equation to calculate the distance traveled by both car and trailer:

$v^2=v_o^2-2ax\\\\x=\frac{-v^2+v_o^2}{2a}$

v: final velocity=0

vo: initial velocity = 72km/h = 60 m/s

by replacing the values of these parameters you obtain for x:

$x=\frac{-0m/s+60m/s}{2(3.46m/s^2)}\\\\x=8.67m$

(b) The horizontal component of the force exerted by the trailer hitch is given by:

$F_T=5000N-4000N=1000N$

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