Bubba is trying to pull his boat out of the lake after a rainy day fishing, but

Question

Bubba is trying to pull his boat out of the lake after a rainy day fishing, but the rain has made the boat ramp muddy and slick enough that he can't back his truck down the hill to attach the boat trailer. Instead he attaches a rope to the back of his truck, runs the rope over a parking barrier, and attaches the other end to the trailer. He can then pull the boat and trailer up the hill with the truck on level ground.

Unfortunately, the rope he uses to do this is the rope that usually attaches the boat to the trailer. The boat is just sitting on the trailer with nothing (but friction) to keep it in place. Of course there is also friction between the trailer and the ramp. Air drag is zero.

What you know is:

Mass of Boat = 170 kg

Mass of Trailer = 340 kg

Mass of Truck = 1950 kg

Angle of ramp = 8 degrees

Coefficent of Static Friction, Boat on Trailer = 0.50

Coefficient of Kinetic (or rolling) Friction, Ramp on Trailer = 0.20

What is the maximum tension that Bubba can give to the rope and get his boat up the ramp without it sliding off the trailer?

Give your answer in Newtons to at least three significant figures to avoid having your answer counted as incorrect due to rounding errors. Your answer will not be graded on the number of significant digits.

Explanation / Answer

Tension = T
Mass of boat, m = 170 kg
Mass of Trailer, m' = 340 kg
Mass of Truck, M = 1950 kg
Angle, theta = 8
mu bota on trailer, mu = 0.5
mu trailer on ramp, mu' = 0.2

Max possible tension is when the boat is about to slip, so the friction on boat is maximum
consider boat as the body
f = m*a + mgsin(theta) = 170a + 231.862 (where a is acc of whole system)
but f = mu N = 0.5*170*9.8cos(8) = 824.893 N
so 170a + 231.862 = 824.893
max a = 3.488m/s/s

Consider trailer as the body
T + f - f' - m'gsin(theta) = (m'+m)a
N = (m'+m)gcos(theta)
f' = mu'*N = 0.2*(170 + 340)*9.8*cos(8) = 989.87 N
T max = 510*3.488 + 340*9.8*sin(8) + 989.87 - (170*3.488 + 231.862) = 2407.6527 N

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.