Sledge 36
Sledge 36
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help with maths: mechanics 1!?
a sledge has a mass 30kg, is pulled in a straight line along horizontal ground by means of a rope. the rope makes an angle 20° with the horizontal. the coefficient of friction between the sledge and the ground is 0.2. the sledge is modelled as a particle and the rope is a light inextensible string. the tension in the rope is 150N.
find,
a) the normal reaction of the ground on the sledge (243N)
b) the acceleration of the sledge (3.08ms^-2)
when the sledge is moving at 12ms^-1, the rope is released from the sledge.
c) find the distance travelled by the sledge from the moment when the rope is released to the moment when the sledge comes to rest (36.7m)
the numbers in the brackets are the answers as given by the book.. i can't seem to get the answer. if anyone could show me how it'd be deeply appreciated 
help with maths: mechanics 1!?
jinshina.
a sledge has a mass 30kg, is pulled in a straight line along horizontal ground by means of a rope. the rope makes an angle 20° with the horizontal. the coefficient of friction between the sledge and the ground is 0.2. the sledge is modelled as a particle and the rope is a light inextensible string. the tension in the rope is 150N.
find,
a) the normal reaction of the ground on the sledge (243N)
Normal Reaction = upward component of the force - weight
Normal Reaction = (30 x 9.8) -150sin 20°
Normal Reaction = (294) - 51.3
======================================
Normal Reaction = 242.7 N ◄• Ans
======================================
b) the acceleration of the sledge (3.08ms^-2)
Force = mass/9.8 (acceleration)
150/(9.8 N/kg)(Cos 20°) = 30/ (9.8 m/sec²) (accelertion)
=======================================
acceleration = 4.69 m/sec² ◄• Ans
=======================================
when the sledge is moving at 12ms^-1, the rope is released from the sledge.
c) find the distance traveled by the sledge from the moment when the rope is released to the moment when the sledge comes to rest (36.7m)
Distance = V(final)² - V(initial)² / 2(acceleration)
Distance = (0)² - (12)² / 2(4.69)
Distance = 144 / 9.38
===========================
Distance = 15.35 m ◄ Ans
===========================
I tried to check the answer of the Book:
Acceleration = 3.08 m/s²
Vi = 12 m/s
by the formula = Distance = [vf² -V²] / 2 (acceleration)
Distance = [0 - 12²]/2(3.08)
Distance = [144]/(6.16)
Distance = 23.38 m ← this is supposed to be the answer for the book. & not (36.7 m)
hope this helps
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