Question

A 5.0-kg object is suspended by a string from the ceiling of an elevator that is accelerating downward at a rate of 2.6 m/s2. What is the tension in the string (in N)?

Answer 1

The tension in the string is 62.0 N.

Step-by-step explanation:

The tension in the string can be determined by considering the forces acting on the object. In this case, the tension force in the string will be equal to the weight of the object plus the force due to its acceleration. The weight of the object can be calculated by multiplying its mass (5.0 kg) by the acceleration due to gravity (9.8 m/s²).

The weight of the object is given by:

Weight = mass × acceleration due to gravity

Weight = 5.0 kg × 9.8 m/s² = 49.0 N

The force due to acceleration is given by:

Force due to acceleration = mass × acceleration

Force due to acceleration = 5.0 kg × 2.6 m/s² = 13.0 N

Therefore, the tension in the string is the sum of the weight and the force due to acceleration:

Tension = Weight + Force due to acceleration

Tension = 49.0 N + 13.0 N = 62.0 N

Answer 2

36N

Step-by-step explanation:

First draw a diagram so you can see which forces act in which direction.

Then define which is your positive direction. I chose the direction of accelleration (downward) to be positive. This means that the weight of the object is also acting in the positive direction but Tension is acting in the negative direction.

If the elevator which contains the object within is accellerating at 2.6 ms^-2 then the object and string system is also accellerating at the same rate.

F = ma where F is the resultant force.

Resultant for is Weight + Tension but tension is in the negative direction so

F = mg -T

F = 5g - T

F = ma so F = 5 x 2.6

13 = 5g-T

T = 5g - 13

T = 36N

(I've taken g = 9.8ms^-2 but if this is for a physics class I'd take it to be 9.81ms^-2)