Answer :
2.69ms2, −2.31ms2, −9.81ms2 and 0ms2 are acceleration (magnitude and direction) when the tension in the rope is 250 N, 150 N, 156 N and 196N respectively.
What is acceleration?
Acceleration is the rate at which an object changes its velocity over time. It is a vector quantity, which means it has both magnitude (speed) and direction. The most common unit of acceleration is meters per second squared (m/s²).
As, ΣFy=may
Using the assumption that positive means up and negative means down, we obtain:
T−mg=may
a) when T=+250:
250−(20)(9.81)=(20) ay
ay=2.69ms2
Provide the direction to your calculator. As my response was affirmative, there is an upward acceleration.
b) when T=+150:
150−(20)(9.81)=(20)ay
ay=−2.31ms2
or
ay=2.31ms2
As my solution was negative.
c) when T=0:
0−(20)(9.81)=(20)ay
ay=−9.81ms2
or
ay=9.81ms2
As my solution was negative.
d) when T=+196:
196−(20)(9.81)=(20)ay
ay=0ms2
Keep in mind that the tension and weight are equivalent while the box is not accelerating.
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