Two blocks, each of mass m = 3.35 kg are hung from the ceiling of an elevator as in the figure below.
(a) If the elevator moves with an upward acceleration a with arrow of magnitude 1.7 m/s2, find the tensions T1 and T2 in the upper and lower strings.
T1 = N
T2 = N
(b) If the strings can withstand a maximum tension of 80.2 N, what maximum acceleration can the elevator have before a string breaks?
(m/s2)
(a) To find the tensions T1 and T2 in the strings, we need to consider the forces acting on each block.
For block 1 (upper block):
1. The weight of the block acts downwards, given by W1 = m * g, where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2).
2. The tension in the upper string (T1) acts upwards.
3. The net force acting on block 1 is the difference between the tension and weight: T1 - W1.
For block 2 (lower block):
1. The weight of the block acts downwards, given by W2 = m * g.
2. The tension in the lower string (T2) acts upwards.
3. The net force acting on block 2 is the difference between the tension and weight: T2 - W2.
Now, let's use Newton's second law, F = ma, to set up equations for each block:
For block 1:
T1 - W1 = m * a
For block 2:
T2 - W2 = m * a
Since the blocks are connected and move together, their accelerations will be the same, denoted as 'a'. Also, both blocks have the same mass, denoted as 'm'. Thus, we can rewrite the equations as:
T1 - m * g = m * a
T2 - m * g = m * a
Now, substitute the given values:
m = 3.35 kg
g = 9.8 m/s^2
a = 1.7 m/s^2
For T1:
T1 - (3.35 kg * 9.8 m/s^2) = (3.35 kg * 1.7 m/s^2)
T1 - 32.83 N = 5.69 N
T1 ≈ 38.52 N
For T2:
T2 - (3.35 kg * 9.8 m/s^2) = (3.35 kg * 1.7 m/s^2)
T2 - 32.83 N = 5.69 N
T2 ≈ 38.52 N
Therefore,
T1 ≈ 38.52 N
T2 ≈ 38.52 N
(b) To find the maximum acceleration before a string breaks, we need to find the tension in either string when it reaches its maximum value.
Given that the maximum tension a string can withstand is 80.2 N, we know that either T1 or T2 cannot exceed this value.
Since T1 = T2 = 38.52 N, we can see that both tensions are below the maximum allowed value. Therefore, there is no need to consider the maximum acceleration in this case, as the strings will not break.
To summarize:
The tensions T1 and T2 are approximately 38.52 N each.
Since T1 and T2 are below the maximum allowed tension of 80.2 N, there is no maximum acceleration to consider in this scenario.
just do thee same old hanging problems with
g = 9.81 + 1.7
or g = 9.81 + A
obviously tension higher in top string