1) Mechanical advantage: 8.5
2) Work output: 110 J
3) Work input: 28.6 J
4) Efficiency: 3.8
Explanation:
1)
The (actual) mechanical advantage of a machine is the ratio between the output force (the load) and the input force (the effort):
where
is the output force
is the input force
For the machine in this problem, we have
(force applied in input)
(output force, equal to the weight of the package which is lifted)
Therefore, the mechanical advantage is
2)
The work output in a machine that lifts an object is equal to the gravitational potential energy gained by the object:
where:
is the output force, which is the weight of the object
h is the change in height of the object
In this problem,
(weight of the package)
h = 2.0 m (change in height of the package)
Therefore, the output work is:
3)
The work input is the amount of work done on the effort side of the machine. For a ramp, is given by:
where
is the force in input (the effort)
L is the length of the ramp
For the ramp in this problem, we have:
(input force)
L = 4.4 m (length of the ramp)
Therefore, the work input is:
4)
The efficiency of a machine is given by
where
is the output work
is the input work
The efficiency of a machine basically represents how much of the input work is transformed into useful output work.
For the ramp in this problem:
Therefore, the efficiency of this machine is
Note that the data given for this machine are unrealistic: in fact, for a real machine, the work output cannot be larger than the input work (and the efficiency cannot be larger than 1), so I assume there is a mistake in one of the numbers given in the problem.
Learn more about work:
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