A lamp hangs vertically from a cord in a descending elevator that decelerates at 2.9 m/s2.
a) If the tension in the cord is 94 N, what is the lamp's mass?
b)What is the cord's tension when the elevator ascends with an upward acceleration of 2.9 m/s2?
1+1=2
To solve these problems, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
a) We are given the tension in the cord, which is 94 N, and the deceleration of the elevator, which is -2.9 m/s^2 (negative because it is decelerating). We need to find the mass of the lamp.
The only force acting on the lamp is the tension in the cord, which is equivalent to the force due to gravity (weight) in this case. Therefore, we can set up the equation:
94 N = m * (-2.9 m/s^2)
Rearranging the equation, we have:
m = 94 N / (-2.9 m/s^2)
m ≈ 32.4 kg
Therefore, the mass of the lamp is approximately 32.4 kg.
b) Now, let's consider the scenario where the elevator is ascending with an upward acceleration of 2.9 m/s^2. We need to find the tension in the cord.
In this case, there are two forces acting on the lamp: the force due to gravity (weight) and the upward force caused by the acceleration of the elevator. The net force acting on the lamp is the sum of these forces.
The force due to gravity can be calculated using the mass of the lamp we found in part a:
Weight = mass * gravity
Weight ≈ 32.4 kg * 9.8 m/s^2 (acceleration due to gravity)
Weight ≈ 317.52 N
The net force is equal to the mass of the lamp multiplied by the acceleration of the elevator, which is 2.9 m/s^2 in this case:
Net force = mass * acceleration
Net force = 32.4 kg * 2.9 m/s^2
Net force ≈ 93.96 N
Now, since the net force is the sum of the forces due to gravity and the upward force caused by acceleration, we can set up the equation:
Tension + Weight = Net force
Tension + 317.52 N = 93.96 N
Tension = 93.96 N - 317.52 N
Tension ≈ -223.56 N
Therefore, the tension in the cord when the elevator ascends with an upward acceleration of 2.9 m/s^2 is approximately -223.56 N. Note that the negative sign indicates that the tension is acting in the opposite direction to the gravity.