A man ties one end of a strong rope 8.17 m long to the bumper of his truck, 0.524 m from the ground, and the other end to a vert
ical tree trunk at a height of 2.99 m. He uses the truck to create a tension of 8.57 102 N in the rope. Compute the magnitude of the torque on the tree due to the tension in the rope, with the base of the tree acting as the reference point.
1 answer:
Answer:
2442.5 Nm
Explanation:
Tension, T = 8.57 x 10^2 N
length of rope, l = 8.17 m
y = 0.524 m
h = 2.99 m
According to diagram
Sin θ = (2.99 - 0.524) / 8.17
Sin θ = 0.3018
θ = 17.6°
So, torque about the base of the tree is
Torque = T x Cos θ x 2.99
Torque = 8.57 x 100 x Cos 17.6° x 2.99
Torque = 2442.5 Nm
thus, the torque is 2442.5 Nm.
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Answer:
3099 J
Explanation:
The increase in thermal energy corresponds to the mechanical energy lost in the process.
The mechanical energy is given by the sum of gravitational potential energy and kinetic energy of the fireman:
At the top of the pole, the fireman has no kinetic energy, so all his mechanical energy is just potential energy:
When the fireman reaches the bottom, he has no gravitational potential energy, so his mechanical energy is just given by his kinetic energy:
So, the loss in mechanical energy was
and this corresponds to the increase in thermal energy.