Answer :
The power needed is 0.0054 hp
Explanation:
First of all, we need to convert the mass from pounds to kilograms:
[tex]m= 10 lb \cdot 0.454 = 4.54 kg[/tex]
Then we have to convert the height from feet to meters:
[tex]h= 3 ft \cdot 0.3048 = 0.91 m[/tex]
The weight of the object is:
[tex]F=mg=(4.54)(9.81)=44.5 N[/tex]
Now we can calculate the work needed to lift the box, which is equal to the change in gravitational potential energy of the object:
[tex]W=Fh=(44.5)(0.91)=40.5 J[/tex]
The power required to lift the object is given by:
[tex]P=\frac{W}{t}[/tex]
where
W = 40.5 J is the work done
t = 10 s is the time taken
Substituting,
[tex]P=\frac{40.5}{10}=4.05 W[/tex]
And finally, we can convert into horsepower, keeping in mind that
1 hp = 746 W
We find
[tex]P=(4.05 W)\cdot \frac{1}{746}=0.0054 hp[/tex]
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