A 41.3 kg wagon is towed up a hill inclined
at 19.6 deg with respect to the horizontal. The
tow rope is parallel to the incline and exerts
a force of 150 N on the wagon. Assume that
the wagon starts from rest at the bottom of
the hill, and disregard friction.
The acceleration of gravity is 9.81 m/s2.
How fast is the wagon going after moving
71.9 m up the hill?
Answer in units of m/s.
at 19.6 deg with respect to the horizontal. The
tow rope is parallel to the incline and exerts
a force of 150 N on the wagon. Assume that
the wagon starts from rest at the bottom of
the hill, and disregard friction.
The acceleration of gravity is 9.81 m/s2.
How fast is the wagon going after moving
71.9 m up the hill?
Answer in units of m/s.
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Alright so the force of gravity is pointing straight down, but has two components, one pointing down the plane, and one pointing into the plane. Since there is no friction, we can disregard the component into the incline, but the other force acts against the 150N up the plane.
150 - m*g*sin(19.6deg) = 14.23N, which is positive and going up the plane.
F = ma, so 14.23 = 41.3a, a = 0.345m/s^2
Vf^2 = Vo^2 + 2*a*x, so Vf = sqrt(2*(.345m/s^2)*(71.9m)) = 7.04m/s
150 - m*g*sin(19.6deg) = 14.23N, which is positive and going up the plane.
F = ma, so 14.23 = 41.3a, a = 0.345m/s^2
Vf^2 = Vo^2 + 2*a*x, so Vf = sqrt(2*(.345m/s^2)*(71.9m)) = 7.04m/s