In the problems below, use g = 9.8 m/s 2 A thief has picked a coffer(a coffer is
ID: 1338331 • Letter: I
Question
In the problems below, use g = 9.8 m/s2
A thief has picked a coffer(a coffer is a box usually used to hold valuables) to steal. To find out how heavy the coffer is, he takes a spring with a spring constant of k = 1340N/m. He fixes one end of the spring to the ceiling and hangs the coffer to the other end vertically.
(a) If the spring extends by a distance of 26.47 cm, what is the mass of the coffer?
kg
Now, the thief pulls the coffer along a frictionless horizontal surface with a rope. The rope makes an angle of 36.8° with respect to the horizontal.
(b) If the tension of the rope is 24.9 N and the work done on the coffer by the rope is 69.78 J, what is the horizontal distance that the thief has pulled the coffer?
m
(c) What is the average power, the average rate at which the work is done on the coffer by the rope?
watts
(d) What is the kinetic energy of the coffer at the end of the pull?
J
Finally, the thief stopped the coffer and lifted it from the floor to put it onto his truck.
(e) If the thief has done a work of 248.33 J to lift the coffer vertically, what is the height that the coffer is lifted to?
m
Explanation / Answer
a) the force acting on th coffer is only gravitational force = mg, equal amount of restoring force develops in the spring
so mg= kx ==> m=kx/g ==> m= 1340*0.2647/9.8 = 36.19 kg
b) here (mg Sin theta +T )x = 69.78 J ===> x= 69.78/(36.19*9.8*0.599+24.9) = 0.2940 m
c) power is work rate power on coffer is 69.78 /1 = 69.78 W
the horizontal distance that the thief has pulled the coffer is 0.2940 m
e) If the thief has done a work of 248.33 J to lift the coffer vertically means the gravitation potential energy is equal to the work done
so mgh= 248.33 J ==> h= 248.33/36.19*9.8 = 0.700 m
he height that the coffer is lifted to is 0.7 m
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