a horse pulls a cart with a force of 30N and at constant speed 7.2KM/HR. with the help of a rope tied to a cart making an angle of 60° with the horizontal for 1 minute. Calculate the work done by the horse and its power?
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Answer:
The horse pulls with a force
F
.
As the cart moves through a displacement
d
, the work done by
F
is W=
F
.
d
=Fdcosϕ, where
ϕ is the angle between
F
.
d
.
(a) In 10 min the cart moves
d=vΔt=(6.0
h
mi
)
(
60min/h
5280ft/mi
)(10min)=5280ft.
so that ,
W=Fd cosϕ=(40 lb)(5280 ft)cos30
0
=1.8×10
5
ft.lb.
(b) The average power is given as.
With Δt=10min=600s, we obtain
P
avg
=
Δt
W
=
600s
1.8×10
5
ft.lb
=305 ft.lb/s,
which (using the conversion factor 1 hp = 550 ft. lb/s found on the inside back cover of the text) converts to P
avg
=0.55hp.
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