Howard is standing in the middle of a skating rink (we ll assume no friction), and his four friends Alice, Bernie, Christopher, and David approach him from each of the four compass directions - north, east, south, and west, respectively.
Alice pushes on Howard with a force of x + 20 Newtons. Bernie pushes on him with a force of 2x + y Newtons. Christopher pushes on him with a force of 2x - y Newtons, and David pushes with a force of 5y Newtons.
Howard, though being pushed from all directions, does not move. Calculate the forces being applied in all four directions.
Forces Problem?
2017-09-26 10:22 pm
回答 (3)
2017-09-26 10:54 pm
Refer to the diagram below.
Along the N-S direction, the resultant force = 0
x + 20 = 2x - y
x - y = 20 …… [1]
Along the W-E direction, the resultant force = 0
5y = 2x + y
2x - 4y = 0
x - 2y = 0 …… [2]
[1] - [2]:
y = 20
Substitute y = 20 into [1]
x - 20 = 20
x = 40
Force applied by Alice from the north = 40 + 20 N = 60 N
Force applied by Bernie from the east = 2 × 40 + 20 N = 100 N
Forced applied by Christopher from the south = 2 × 40 - 20 N = 60 N
Forced applied by David from the west = 5 × 20 N = 100 N
Along the N-S direction, the resultant force = 0
x + 20 = 2x - y
x - y = 20 …… [1]
Along the W-E direction, the resultant force = 0
5y = 2x + y
2x - 4y = 0
x - 2y = 0 …… [2]
[1] - [2]:
y = 20
Substitute y = 20 into [1]
x - 20 = 20
x = 40
Force applied by Alice from the north = 40 + 20 N = 60 N
Force applied by Bernie from the east = 2 × 40 + 20 N = 100 N
Forced applied by Christopher from the south = 2 × 40 - 20 N = 60 N
Forced applied by David from the west = 5 × 20 N = 100 N
2017-09-26 10:39 pm
It is very unfortunate that the person who constructed this question chose the names x and y for the unknowns, as those names suggest directions which, however, I think are not intended.
I THINK what is intended is that Alice pushes south, Bernie pushes west, Chris pushes north, and David pushes east. If so, you have
x + 20 = 2x - y, and
2x + y = 5y.
From the latter equation you have
x = 2y, and so the first equation gives you
2y + 20 = 4y - y => y = 20 => x = 40.
Alice and Chris are each pushing with a force of 60N, while Bernie and David are each pushing with a force of 100N.
I THINK what is intended is that Alice pushes south, Bernie pushes west, Chris pushes north, and David pushes east. If so, you have
x + 20 = 2x - y, and
2x + y = 5y.
From the latter equation you have
x = 2y, and so the first equation gives you
2y + 20 = 4y - y => y = 20 => x = 40.
Alice and Chris are each pushing with a force of 60N, while Bernie and David are each pushing with a force of 100N.
2017-09-26 10:31 pm
Since Howard does not move, the forces in each direction much add up to zero.
North/south: x + 20 = 2x - y
East/west: 2x + y = 5y
Now it's just algebra.
North/south: x + 20 = 2x - y
East/west: 2x + y = 5y
Now it's just algebra.
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