Stevedore (Physics Puzzle For Fun)?

Question

The stevedore is loading 100-pound drums on a truck by rolling them up a ramp. The truck bed is 3 feet above the street and the ramp is 6 feet long. How much force must the stevedore exert on the drums as she goes up the ramp?

a) 200 lb
b) 100 lb
c) 50 lb
d) 10 lb
e) Can't say

The answer is C. The 100-lb drums end up 3 ft higher than they were, so they end up with 3 ft x 100 lb = 300 ft lb more energy. Now what force exerted over the 6 ft legnth of the ramp will give 300 ft lb of work? It must be 50 lb of force because 6 ft x 50 lb = 300 ft lb. Three comments:
1) Most books solve this type of problem using a different method that involves vectors. To see how vectors are used to solve this type of problem, look at various books. It's important to see things from different points of view. And it's nice to see that different viewpoints support the same conclusion.
2) If you can't add apples and oranges or feet and pounds, how come you can multiply them?
3) The idea of the inclined plane or ramp is basically the same as the idea that underlies the lever or see-saw and block and tackle or compound pulley. In each case the force necessary to do a certain amount of work is reduced by increasing the distance over which the force acts. (Continued)...

(Continued)
To lift the drum 3 ft requires only half as much force when moved twice as far (6 ft) on the inclined ramp. If lifting a heavy man on a see-saw a distance of one inch requires that a kid go down three inches, then the weight of the kid need only be one third the weight of the man. Pulleys work on the samme principle.

Answer 1

The best answer, given the informatioon available, is C, 50 pounds. No information was given by which a friction force could be computed; therefore, as in some classical physics problems, friction is assumed to be zero, unless you are looking for the answer E, Can't say. The solution is simply a matter of understanding the proportions involved in resolving the drum weight (downward force vector) into its component force vector parts. We are looking for the force vector parallel to the ramp surface needed to push each drum up the ramp. I determined the component force vector parts as follows. The vertical force of 100 pounds is to the 3 foot high truck bed (vertical distance) as the unknown force up the ramp is to the 6 foot long ramp. Solving for the unknown force up the ramp gives answer C, 50 pounds. Given the simple numbers (like many classic physics problems), it's a simple mental exercise using physics principles. I didn't have the time to derive the "ratio" relationship from the fundamental equations, so this may not be the "best" explanation/answer. Even if the force is applied at the top of the drum, which gives an answer of 25 pounds, compared to my answer of 50 pounds when force is applied at the drum center of gravity, the principle is the same except for the mechanical advantage when the force is applied at the drum top. The more I look at this problem, the more I'm beginning to think Dr H is looking for answer E, Can't say. I'm going with answer E, Can't say...Final answer.

Answer 2

Assuming there is no rolling resistance, the force needed to push an object up an ramp is

F = m*g*sin(theta)
F = W*sin(theta)

where W is the weight, and theta is the inclination of the ramp.

Your ramp is 3 feet tall, and 6 feet long on the diagonal (that's how I read the question, anyway). By the Pythagorean theorem, the horizontal ramp length is 3*sqrt(3), making the ramp angle

theta = arctan(3 / (3*sqrt(3)))
theta = arctan(1 / sqrt(3))
theta = pi / 6 radians

So, the force required is

F = (100 lbs) * sin(pi / 6)
F = (100 lbs) * 1/2
F = 50 lbs

Answer 3

Dums are not frictionlessly sliding blocks.
Lets assume that friction is sufficient (μ > 1/√12)

If the stevedore excerts the force at the _top of the
drum the force required will be only half of the force
applied at the center.

All in all minimal force required is 25 lb
applied over displacement of 6ft x 2 = 12 ft.
(the top of the drum has twice the velocity of the center)

So the answer is

f) none of the above

Answer 4

More than 50 lbs.

There is friction and other forces at work as well as just lifting the drums.

Answer 5

yet another element I word is with vocabulary too. as an occasion, whilst i'm out on the floor designing a restoration and the save workers inquire from me why that's or something to that result it form of looks like I have not any issues looking the awesome words to describe the physics at the back of each and every restoration. in spite of the undeniable fact that, once I could desire to articulate activities and such I truly have a complicated time looking the awesome words to tricky on the region. i come across myself giving dissimilar "umm"'s and "ahh"s as fillers on an identical time as i attempt to extract the awesome adjective or adverb from my suggestions. I additionally think of I truly have some upload additionally. My interest span infrequently lasts for greater suitable than 10 minutes in the previous I start up day dreaming and miss the presentation all jointly. So whilst i'm in mattress i choose the television on or some track to maintain my suggestions at bay in any different case i would be up all night taking part in the day's activities in my head lower back and lower back or dreaming (without napping) concerning the destiny. i could even think of a pair of physics subject from the day. EDIT: BTW Remo, whilst i became working that subject out the day previous I did see that the circulate situations have been the comparable for the two pipes once I plugged in 10L, yet i assumed there became yet another trick so which you probably did get me. on an identical time as i attempt to apply the awesome vocab once I form I do word the situation you talk of in different aspects of my existence. great assertion.