Acceleration of the table: B. 0.50 meters/second2
Explanation:
The problem can be solved by using Newton's second law of motion, which states that the net force acting on an object is the product of its mass and its acceleration. Mathematically:
where
is the net force
m is the mass
a is the acceleration
For the table in this problem, we have:
is the net force on the table, because there are two forces of 125 N and 120 N acting in opposite directions
m = 10.0 kg is the mass of the table
Solving for a, we find the acceleration:
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We can use the formula of the moment of inertia given by:
Where:
r = Distance from the point about which the torque is being measured to the point where the force is applied
F = Force
I = Moment of inertia
α = Angular acceleration
So:
Answer:
12 rad/s²
The kinetic energy halfway the hill is
Explanation:
If there are no friction forces acting on the cart, we can apply the law of conservation of energy: the mechanical energy of the cart (which is the sum of potential energy + kinetic energy) must be conserved. So we can write:
where
is the initial potential energy, at point A, with
m = 980 kg (mass of the cart)
(acceleration of gravity)
(height at point A)
is the initial kinetic energy, at point A
, with
(velocity at point A)
is the final potential energy, at point B, where
(height at point B)
is the final kinetic energy, at point B, where
is the velocity at point B
Here we are interested in finding , so by re-arranging the equation and substituting we find:
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