What force (in newtons) is required to accelerate a body with a mass of 32 kilograms at a rate of 12 m/s2? If a body with a mass
1 answer:
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1) The minimum force needed is 920 N
2) The minimum force is 460 N
3) The minimum force is 598 N
Explanation:
1)
We can answer this part by simply looking at the forces involved. In fact, there are two forces acting on the railroad:
- Its weight, W, acting downward
- The force applied to lift it, F, upward
So the net force on the railroad is
where
W = 920 N is the weight of the railroad
In order to lift the railroad, the net force must be upward, so
And therefore
which means that the minimum force needed is equal to the weight of the railroad, 920 N.
2)
In this case, we have to use the principle of equilibrium of moments.
In fact, when the railroad rotates uniformly (=constant angular speed) about its end, it means that the moment produced by the weight (acting in one direction) is equal to the moment produced by the force applied (acting in the other direction). Therefore, we can write:
where
W = 920 N is the weight
L = 2.6 m is the length of the railroad
F is the force applied
We wrote L/2 on the left of the equation because the weight acts at the center of mass of the railroad (located at the midpoint), while on the right it is L because the force F is applied at the end of the railroad.
Solving for F,
3)
This problem is similar to the previous part, however in this case, the force applied F is applied 0.6 m from the end, pivoting around the opposite end.
This means that the distance between the point of application of the force F and the pivot is
L' = L - 0.6
where
L = 2.6 m
Therefore the equation for the equilibrium of moments becomes
and substituting
W = 920 N
L = 2.6
We find the magnitude of F:
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