Removing a Slump A farmer wishes to remove a stump from a field by pulling it out with his tractor. Having removed many stumps before, he estimates that he will need 6 tons (12,000 pounds) of force to remove the stump. However, his tractor is only capable of pulling with a force of 7000 pounds, so he asks his neighbor to help. His neighbor’s tractor can pull with a force of 5500 pounds. They attach the two tractors to the stump with a 40 ∘ angle between the forces, as shown in the figure. (a) Assuming the farmer's estimate of a needed 6-ton force is correct, will the farmer be successful in removing the stump? Explain. (b) Had the farmer arranged the tractors with a 25 ° angle between the forces, would he have been successful in removing the stump? Explain.
Removing a Slump A farmer wishes to remove a stump from a field by pulling it out with his tractor. Having removed many stumps before, he estimates that he will need 6 tons (12,000 pounds) of force to remove the stump. However, his tractor is only capable of pulling with a force of 7000 pounds, so he asks his neighbor to help. His neighbor’s tractor can pull with a force of 5500 pounds. They attach the two tractors to the stump with a 40 ∘ angle between the forces, as shown in the figure. (a) Assuming the farmer's estimate of a needed 6-ton force is correct, will the farmer be successful in removing the stump? Explain. (b) Had the farmer arranged the tractors with a 25 ° angle between the forces, would he have been successful in removing the stump? Explain.
Solution Summary: The author analyzes how a farmer estimates that he will need 6tons of force to remove the stump, but his neighbor's tractor can pull with 5500 pounds.
Removing a Slump A farmer wishes to remove a stump from a field by pulling it out with his tractor. Having removed many stumps before, he estimates that he will need 6 tons (12,000 pounds) of force to remove the stump. However, his tractor is only capable of pulling with a force of 7000 pounds, so he asks his neighbor to help. His neighbor’s tractor can pull with a force of 5500 pounds. They attach the two tractors to the stump with a
angle between the forces, as shown in the figure.
(a) Assuming the farmer's estimate of a needed 6-ton force is correct, will the farmer be successful in removing the stump? Explain.
(b) Had the farmer arranged the tractors with a
angle between the forces, would he have been successful in removing the stump? Explain.
A company specializing in lubrication products for vintage motors produce two
blended oils, Smaza and Nefkov. They make a profit of K5,000.00 per litre of
Smaza and K4,000.00 per litre of Nefkov. A litre of Smaza requires 0.4 litres of
heavy oil and 0.6 litres of light oil. A litre of Nefkov requires 0.8 litres of heavy oil
and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of
light oil. How many litres of each product should they make to maximize profits
and what level of profit will they obtain? Show all your workings.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
Chapter 9 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.