Final answer:
The tension in the cord of a lamp hanging in a decelerating elevator can be found using Newton's second law of motion. Assuming a deceleration of 1.0 m/s² and a mass of 2.0 kg, the tension in the cord is calculated to be 17.6 N.
Step-by-step explanation:
To find the tension in the cord of a lamp hanging in a decelerating elevator, we can apply Newton's second law of motion to the hanging mass. If we assume that the elevator decelerates at 1.0 m/s2, and the mass of the lamp is 2.0 kg, like in the given information, we can calculate the tension as follows:
- First, identify the forces acting on the mass: the gravitational force (weight) and the tension in the cord.
- The gravitational force is calculated by multiplying the mass by the acceleration due to gravity, g (weight = mass × g, with g = 9.8 m/s2).
- Apply Newton's second law (F_net = mass × acceleration), where F_net is the net force acting on the mass.
- Since the elevator is decelerating upwards, the net force is actually less than the weight, and thus the tension is equal to the weight minus the force due to the elevator's deceleration.
- Plugging in the given values, the tension (T) is T = mass × (g - elevator's deceleration).
- The tension can now be calculated as T = 2.0 kg × (9.8 m/s2 - 1.0 m/s2) = 2.0 kg × 8.8 m/s2 = 17.6 N.
In conclusion, the tension in the cord while the elevator decelerates at 1.0 m/s2 is 17.6 N.