6 Simple machine (Inclined plane Lever) – Problems and Solutions
1.
Which inclined plane have the same mechanical advantage
А. (1) и (2)
Б. (1) и (3)
С. (2) и (3)
Д. (2) и (4)
Решение
The inclined plane is one of the simple machines. Simple machines are tools that help people do a job. The inclined plane is used to make it easier for humans to raise an object to a certain height.
The mechanical advantage of the наклонная плоскость is the comparison of the length of the incline to the height of the incline.
The mechanical advantage of the incline plane 1 = 50 cm / 30 cm = 5/3
The mechanical advantage of the incline plane 2 = 5 cm / 4 cm = 5/4
The mechanical advantage of the incline plane 3 = 50 cm / 40 cm = 5/4
The mechanical advantage of the incline plane 4 = 5 cm / 3 cm = 5/3
2.
Distance AB = BC = CD = DE, determine the input force that must be given at point E in order for a balanced lever.
Известно:
AB = BC = CD = DE = l
Distance between output force and fulcrum (a) = л
Distance between input force and fulcrum (b) = 3l
Выходная сила (w) = 900 Newton
В розыске: Сила (F)
решение:
The mechanical advantage :
MA = b / a = 3l/l = 3
Magnitude of force :
MA = w / F
F = w / MA
F = 900 Ньютонов / 3
F = 300 Ньютон
3.
In order for the lever to be balanced then determine the magnitude of свою input force.
Решение
Determine distance between input force and fulcrum (b)
Известно:
Distance between output force and fulcrum (a) = 25 см
Выходная сила (w) = 480 Newton
Входная сила (F) = 160 Н
В розыске: distance between input force and fulcrum (b)
решение:
The mechanical advantage :
MA = w / F = 480 N / 160 N = 3
distance between input force and fulcrum (b)
MA = b / a
3 = b / 25 см
b = (3)(25 см)
b = 75 см
Determine magnitude of force (F)
Известно:
Distance between output force and fulcrum (a) = 25 cm – 10 cm = 15 cm
Object’s weight (w) = 480 Newton
Distance between input force and fulcrum (b) = 75 см
В розыске: Входная сила (F)
решение:
Mechanical advantage :
MA = b / a
MA = 75 cm / 15 cm
MA = 5
Величина силы (Ф):
MA = w / F
F = w / MA
F = 480 Ньютонов / 5
F = 96 Ньютон
In order for the lever to be in a balanced position then input force is reduced 64 Newton (160 N – 96 N).
4. The ratio of the lengths of a and b in figure below is a: b = 1: 2.2. The minimum value of force F to lift the object B with weight of 330 Newtons is …. Newton
100
Б. 150
С. 2200
Д. 7260
Известно:
Расстояние между output force and fulcrum (a) = 1
Distance between input force and fulcrum (b) = 2.2
Вес (w) = 330 Newton
В розыске: Input force (F)
решение:
The mechanical advantage of a lever :
MA = w / F = b / a
МА = механическое преимущество, w = weight, F = input force, b = distance between input force and fulcrum, a = distance between output force and fulcrum
w / F = b / а
330 / F = 2.2 / 1
330 / F = 2.2
330 / 2.2 = F
F = 150 Ньютон
Правильный ответ - Б.
5. A student push an object with a force of F from point A to point B, as shown in figure below. If the трение between object and boar ignored, determine the mechanical advantage.
4
B. 5 / 3
C. 5 / 4
D. ¾
Известно:
Height of inclined plane (y) = 4 meters – 1 meters = 3 meters
Length of horizontal plane (x) = 4 meters
Разыскивается: Механическое преимущество (МА)
решение:
Calculate the length of the inclined plane using the equation of Пифагор :
R = √32+42 = √9+16 = √25 = 5 meters
The mechanical advantage of the inclined plane :
KM = R / y
KM = 5 meters / 3 meters
КМ = 5/3
Правильный ответ - Б.
6. The mechanical advantage of a lever can be increased by…
A. Shorten the path of the incline
B. enlarge the angle of the incline
C. minimize the angle of the incline
D. reduces the force used to move objects
решение:
The equation of mechanical advantage of the inclined plane :
Mechanical advantage = length of inclined plane/height of the inclined plane
– The mechanical advantage is directly proportional to the length of the inclined plane and therefore the mechanical advantage is enlarged if the length of the incline is enlarged.
– The mechanical advantage is inversely proportional to the height of the inclined plane, therefore, the mechanical advantage is minimized if the height of the inclined plane is enlarged and the mechanical advantage is enlarged if the height of the incline is reduced.
– If the angle is minimized then the height of the inclined plane is reduced. The mechanical advantage is enlarged if the height of the inclined plane is reduced. Hence if the angle is minimized then the mechanical advantage is enlarged.
If the angle is enlarged then the height of the inclined plane is enlarged. The mechanical advantage is minimized if the height of the inclined plane is enlarged. Hence if the angle is enlarged then the mechanical advantage is minimized.
Правильный ответ - С.
