Video Transcript
A body was descending vertically in a liquid such that it was covering equal distances in each consecutive time interval of equal length. Given that the weight of the body was 55 kilogram-weight, find the magnitude of the resistive force of the liquid acting against the motion of the body.
Let’s draw a little sketch showing what’s going on here. Here is the body descending vertically in some liquid. We’re given the weight of the body. This is essentially the downward force of its mass due to gravity. So the downwards force of the body is 55 kilogram-weight. But the liquid is also exerting a force on the body itself. This will be acting in the opposite direction to the downwards force of the weight. So let’s call that 𝑅.
Next, what does it mean if the body covers equal distances in each consecutive time interval of equal length? Well, this tells us that the velocity of the body is constant. In other words, it has zero acceleration. Now, if the acceleration of the body is zero and it has constant velocity, then we can say that the sum of the forces acting on that body must be equal to zero. Now, in this case, because we’re acting in a single straight line, we don’t actually need to worry about the vector force. Instead, we just find the resultant force in the vertical direction on the body.
Taking the downwards direction to be positive, since this is the direction in which it’s moving, we can say that the sum of the forces must be 55 minus 𝑅. But this, of course, is equal to zero. So zero is equal to 55 minus 𝑅. We can solve this equation for 𝑅 by simply adding 𝑅 to both sides, giving us 𝑅 is equal to 55. The units here match the units of the weight, so the magnitude of the resistive force of the liquid that acts against the motion of the body is 55 kilogram-weight.
