A crate is subjected to a force of magnitude F = [150/s] N having a constant direction and where s is measured in meters.The mass of the crate is 2-kg and when s = 2 m, the crate is moving to the left with a speed of 4 m/s. Determine its speed when s = 6 m. The coefficient of kinetic friction between the crate and the ground is mk = 0.5.
1) 11.6 m/s
Equation of motion:
Since the crate slides, the friction force developed between the crate
and its constant surface is
Principle of work
and energy : The horizontal component of force F which acts in the direction
of displacement does positive work.
The normal reaction N, the vertical component of force F and the weight of the crate do not displace hence do not work. Applying the conservation of energy principle we have:
T1 + S U1-2 = T2
1/2 (2) 42 +
So the speed of the
crate when s = 6m is,