Two crates of fruit are released from the top of a ramp inclined at 25 degrees from the horizontal and 2.5 meter long. The two crates consist of an apple crate of mass 35 kg that is placed in front of a watermelon crate of mass 80 kg. The apple crate has a coefficient of friction of 0.20 while the watermelon crate has a coefficient of friction of 0.15. How long does it take the apple crate to reach the bottom of the incline if it needs to travel a distance of 2.5 meters?

1 answer

first find the retarding force on each.
watermelon: 80*.15*9.8*cos25deg=106.6N
apple: 35*.2*9.8cos25deg=62.2N
then, find the accelerating force on each.
watermellion=80*9.8*sin35deg-62.2= 387.5
apple: 35*9.8*sin35-62.2=134N
then we have to test if the apple goes fastest:
Accapplie=134/35=3.82 m/s^2
Awater=388/80=4.85 m/s^2
so, the watermellon is pushing the apple...
for the system joined,
acceleration=netforce/total mass=(388+134)/(115)=4.54m/s^2
time...
d=1/2 a t^2 or t= sqrt(2ad) you know a, and d.