Question

A sphere of mass of 1.55 kg is accelerated upwards by a string to which the sphere is attached. Its speed increases from 2.81 m/s to 4.60 m/s in a time of 2.64 s. Calculate the tension in the string, assuming that the tension remains constant during that time.

Answer 1

The tension in the string is 16.24 N

Step-by-step explanation:

Given;

mass of the sphere, m = 1.55 kg

initial velocity of the sphere, u = 2.81 m/s

final velocity of the sphere, v = 4.60 m/s

duration of change in the velocity, Δt = 2.64 s

The tension of the string is calculated as follows;

`T = ma + mg\\\\T = m(a + g)\\\\where;\\\\a \ is \ upward \ acceleration \ of \ the \ sphere\\\\g \ is \ acceleration \ due \ to \ gravity =9.8 \ m/s^2\\\\a = (\Delta V)/(\Delta t) = (v- u)/( t) = (4.6 - 2.81 )/(2.64) = 0.678 \ m/s^2`

T = 1.55(0.678 + 9.8)

T = 1.55(10.478)

T = 16.24 N

Therefore, the tension in the string is 16.24 N