1) The velocity ratio is [tex]500\pi[/tex]
2) The mechanical advantage is [tex]350 \pi[/tex]
3) The effort required is 6.2 N
4) The work done by the effort is 2922 J
Explanation:
1)
The velocity ratio of a screw jack is given by the equation:
[tex]VR=\frac{2\pi L}{p}[/tex]
where:
L is the length of the tommy bar
p is the pitch
For the screw jack in this problem, we have
L = 50 cm (length of the tommy bar)
p = 2 mm = 0.2 cm (pitch)
Therefore, the velocity ratio is
[tex]VR=\frac{2\pi (50)}{0.2}=500 \pi[/tex]
2)
Since the velocity ratio of the screw jack represents its ideal mechanical advantage, the efficiency of the machine is the ratio between the mechanical advantage and the velocity ratio:
[tex]\eta = \frac{MA}{VR}[/tex]
where
MA is the mechanical advantage
VR is the velocity ratio
In this problem, we have:
[tex]\eta = 0.70[/tex] (efficiency is 70%)
[tex]VR=500 \pi[/tex]
Therefore, the mechanical advantage here is
[tex]MA=\eta VR = (0.70)(500 \pi)=350\pi[/tex]
3)
The mechanical advantage of the screw jack can be written as
[tex]MA=\frac{Load}{Effort}[/tex]
where
Load is the force in output
Effort is the input force
Here we know that the Load is the weight of the block lifted by the screw jack:
[tex]Load = mg[/tex]
where
m = 700 kg is the mass
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Substituting,
[tex]Load=(700)(9.8)=6860 N[/tex]
We also know that
[tex]MA=350 \pi[/tex]
Therefore, we can find the effort required:
[tex]Effort = \frac{Load}{MA}=\frac{6860}{350\pi}=6.2 N[/tex]
4)
The work done on the load is given by
[tex]W=(Effort)\cdot d_{eff}[/tex] (1)
where
Effort is the input force
[tex]d_{eff}[/tex] is the distance on the effort side
The velocity ratio can also be rewritten as
[tex]VR=\frac{d_{eff}}{d_{load}}[/tex]
Therefore we can rewrite the distance on the effort side as
[tex]d_{eff} = VR\cdot d_{load}[/tex]
So eq.(1) becomes
[tex]W=(effort)\cdot VR \cdot d_{load}[/tex]
where we have:
[tex]effort = 6.2 N\\VR = 500 \pi\\d_{load}=30 cm = 0.30 m[/tex]
Substituting,
[tex]W=(6.2)(500\pi)(0.30)=2922 J[/tex]
Learn more about simple machines:
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