Two blocks each of mass 3.34 kg are fastened to the top of an elevator as in the figure. (a) If the elevator accelerates upward at 1.31 m/s2, find the tensions T1 and T2 in the upper and lower strings.
(p4.21a1), enter the answer for T2, the tension in the cable holding the lower block
(p4.21a2), enter the answer for T1, the tension in the cable holding the upper block
To find the tensions T1 and T2 in the upper and lower strings, we can use Newton's second law. Here are the steps to get the answers:
1. Calculate the gravitational force acting on each block:
The gravitational force on each block is given by F = m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2). Since both blocks have the same mass of 3.34 kg, the gravitational force on each block is:
F_gravity = 3.34 kg * 9.8 m/s^2 = 32.732 N
2. Determine the net force on each block:
The net force on each block is the sum of the tension force and the gravitational force. Since the elevator is accelerating upward at 1.31 m/s^2, the net force on each block is:
F_net = m * (g + a), where a is the acceleration of the elevator. Substituting the values:
F_net = 3.34 kg * (9.8 m/s^2 + 1.31 m/s^2) = 37.327 N
3. Find the tension in the lower string (T2):
The tension in the lower string is equal to the net force on the lower block. So, T2 = F_net = 37.327 N. This is the answer for (p4.21a1).
4. Find the tension in the upper string (T1):
Since the upper and lower strings are connected to the same elevator, they experience the same tension force. Therefore, T1 is also equal to 37.327 N. This is the answer for (p4.21a2).