help with math?

2020-04-03 10:30 pm
A 2.1-kg block is kept on a 3.5-kg block resting on the floor of an elevator. If the elevator is moving up at 1.1
m/s2
calculate the following
a. Force exerted by the 2.1-kg block on the 3.5-kg block.
b. Force exerted by the floor of the elevator on the 3.5-kg block.

回答 (3)

2020-04-03 11:37 pm
✔ 最佳答案
a.Refer to the diagram below.
Take g = 9.8 m/s²

Force exerted to the 2.1-kg block:
Weight of the 2.1 kg block (downward) = 2.1g
Force exerted by the 3.5-kg block (upward) = R₁

F = ma
R₁ - mg = ma
R₁ - 2.1 × 9.8 = 2.1 × 1.1
Force exerted by the 3.5-kg block on the 2.1-kg block, R₁ = 22.9 N

The two forces in blue are action and reaction repectively.
Hence, force exerted by the 2.1-kg block on the 3.5-kg block, R₁ = 22.9 N ≈ 23 N (to 2 sig. fig.)

====
b.
Force exerted to the 3.5-kg block:
Weight of the 3.5-kg block (downward) = 3.5g
Force exerted by the 2.1-kg block (downward), R₁ = 22.9 N
Force exerted by the floor of the elevator (upward) = R₂

F = ma
R₂ - R₁ - mg = ma
R₂ - 22.9 - 3.5 × 9.8 = 3.5 × 1.1
Force exerted by the floor of the elevator on the 3.5-kg block = 61 N (to 2 sig. fig.)

Alternative method:
Consider the two blocks as a whole system:
Weight of the blocks (upward) = (2.1 + 3.5)g = 5.6g
Force exerted by the floor of the elevator (upward) = R₂

F = ma
R₂ - mg = ma
R₂ - 5.6 × 9.8 = 5.6 × 1.1
Force exerted by the floor of the elevator on the 3.5-kg block = 61 N (to 2 sig. fig.)
2020-04-03 10:48 pm
the elevator is moving upward at 1.1 m/s
or
the elevator is accelerating upward at 1.1 m/s²
?

I'll assume the second. 

add gravity, and acceleration is 9.8+1.1 = 10.9 m/s²
F = ma = 2.1 kg x 10.9 m/s² = 23 N
b) F = ma = (2.1+3.5) kg x 10.9 m/s² = 61 N
2020-04-03 10:46 pm
These types of problems are of course solved using F = m*a.  Two of the three gives the third.
F = m(g+a) = 2.1(9.8+1.1) = 22.9N <<<<< a.
F = m(g+a) = (3.5+2.1)(9.8+1.1) = 61N <<<< b.


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