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A block lies on a smooth plane tilted at an angle = 29.0° to the horizontal. Ignore friction?
A block lies on a smooth plane tilted at an angle = 29.0° to the horizontal. Ignore friction.
a) Determine the acceleration of the block as it slides down the plane.
(b) If the block starts from rest 8.70 m up the plane from its base, what will be the block's speed when it reaches the bottom of the incline?
Sum of the forces parallel to the plane is only the parallel component of the force of weight
force of weight = mg. g = 9.8 m = mass
the parallel component would be mg * sin 29
Sum of the forces = ma a = acceleration
mg * sin 29 = ma ~ m's cancel
g*sin 29= a
a = 4.75
b) use energy.
change in potential energy = change in kinetic energy
it starts with no kinetic energy, only potential. When it ends it has no potential only energy
potential energy kinetic
mgh = .5mv^2 m's cancel
gh = .5 v^2
2gh = v^2
2 * 9.8 * 8.7 = v^2
170.52 = v^2 squareroot
13.06 m/s = v
Significant figures wise v = 13m/s