a worker poling a boat—a very efficient mode of transportation—across a shallow
ID: 1356098 • Letter: A
Question
a worker poling a boat—a very efficient mode of transportation—across a shallow lake. He pushes parallel to the length of the light pole, exerting a force of magnitude 235 N on the bottom of the lake. Assume the pole lies in the vertical plane containing the keel of the boat. At one moment, the pole makes an angle of 35.5° with the vertical and the water exerts a horizontal drag force of 47.5 N on the boat, opposite to its forward velocity of magnitude 0.857 m/s. The mass of the boat including its cargo and the worker is 373 kg.
(a) The water exerts a buoyant force vertically upward on the boat. Find the magnitude of this force.
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N
(b) Model the forces as constant over a short interval of time to find the magnitude of the velocity of the boat 0.465 s after the moment described.
m/s
Explanation / Answer
(a)
With the x axis horizontally forward, the pole force on the boat is
(235 cos35.5 °ˆj + 235 sin35.5°ˆi) N = (191.3 ˆi + 136.4 ˆj) N
The gravitational force of the whole Earth on boat and worker is
Fg = mg = 373 kg (9.8 m/s2) = 3655.4 N down.
The acceleration of the boat is purely horizontal, so
Fy = +B + 136.4 – 3655.4 = 0
Therefore, the buoyant force: B = 3.52 x 103 N
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(b)
The acceleration is given by
F x = max : + 191.3 N 47.5 N = (373 kg)a
Solve for a
a = 0.385 m/s2
Use kineamtic equation
vx f = vxi + axt
= 0.857 m/s + (0.385 m/s2 )(0.465 s)
Solve for speed
vx f = 1.04 m/s
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