A lamp is suspended by a massless string from the ceiling of a descending elevator which decelerates at 1.6 m/s2. If the tension in the string is 82.0 N, what is the mass of the lamp?
To find the mass of the lamp, we need to use Newton's second law of motion, which states that the sum of all forces acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's break down the forces acting on the lamp. There are two forces at play: the tension in the string and the force due to gravity.
The tension force is simply the force that the string exerts on the lamp, which we know is 82.0 N.
The force due to gravity is the weight of the lamp, given by the equation F = m * g, where F is the force due to gravity, m is the mass of the object, and g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Now, since the elevator is descending and decelerating, the acceleration of the lamp is equal to the deceleration of the elevator, but in the opposite direction. So, the acceleration of the lamp is -1.6 m/s^2.
Using Newton's second law, we can write the equation:
Tension force + Force due to gravity = mass * acceleration
Substituting the given values into the equation:
82.0 N + (mass * 9.8 m/s^2) = mass * (-1.6 m/s^2)
Simplifying the equation:
82.0 N + 9.8 m/s^2 * mass = -1.6 m/s^2 * mass
Rearranging the equation to isolate the mass term:
82.0 N = -1.6 m/s^2 * mass - 9.8 m/s^2 * mass
82.0 N = -11.4 m/s^2 * mass
Dividing both sides of the equation by -11.4 m/s^2:
mass = 82.0 N / -11.4 m/s^2
mass ≈ -7.19 kg
Since mass cannot be negative in this case, we can ignore the negative sign and take the absolute value:
mass ≈ 7.19 kg
Therefore, the mass of the lamp is approximately 7.19 kg.