Question

7. A package weighing 55 N is lifted to a height of 2.0 m by pulling it up a ramp
4.4 m long. The person pulling the package exerts a force of 6.5 N.
a. What is the mechanical advantage of the ramp?
c.
What is the work output?
winston What is the work input?
- wout foutt dout
What is the efficiency of the machine?

Answer 1

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):

$MA=\frac{F_{out}}{F_{in}}$

where

$F_{out}$ is the output force

$F_{in}$ is the input  force

For the machine in this problem, we have

$F_{in}=6.5 N$ (force applied in input)

$F_{out}=55 N$ (output force, equal to the weight of the package which is lifted)

Therefore, the mechanical advantage is

$MA=\frac{55}{6.5}=8.5$

2)

The  work output in a machine that lifts an object is equal to the gravitational potential energy gained by the object:

$W_{out} = F_{out} h$

where:

$F_{out}$ is the output force, which is the weight of the object

h is the change in height of the object

In this problem,

$F_{out}=55 N$ (weight of the package)

h = 2.0 m (change in height of the package)

Therefore, the output work is:

$W_{out}=(55)(2.0)=110 J$

3)

The work input is the amount of work done on the effort side of the machine. For a ramp, is given by:

$W_{in}=F_{in}L$

where

$F_{in}$ is the force in input (the effort)

L is the length of the ramp

For the ramp in this problem, we have:

$F_{in} = 6.5 N$ (input force)

L = 4.4 m (length of the ramp)

Therefore, the work input is:

$W_{in}=(6.5)(4.4)=28.6 J$

4)

The efficiency of a machine is given by

$\eta=\frac{W_{out}}{W_{in}}$

where

$W_{out}$ is the output work

$W_{in}$ 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:

$W_{out}=110 J$

$W_{in}=28.6 J$

Therefore, the efficiency of this machine is

$\eta=\frac{110}{28.6}=3.8$

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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