A block of weight 45.7 N is hanging from a rope. The tension from the rope is pulling upward on the block. The block is accelerating upward at a rate of 1.50 m/s2. What is the magnitude of the tension in the rope

Let's use Newton's second law of motion here which states that the resultant force (∑F) acting on a body is the product of the mass (m) of the body and the acceleration (a) due to this force. i.e

∑F = m x a ---------------------(i)

Now, let's get the resultant force;

Two main forces are acting on the rope;

i. the weight (W) of the block acting downwards.

Where;

W = mass of block(m) x gravity(g) = m x g

ii. the tension (T) in the rope acting upwards.

Therefore, the resultant force is the vector sum of these two forces as follows;

∑F = - W + T [upward motion is taken as positive. hence -W and +T]

Substitute ∑F = - W + T into equation (i) as follows;

- W + T = m x a ---------------------(ii)

From the question;

* Weight (W) of the block = 45.7N

=> mass (m) of the block = W / g = 45.7 / 10 [Taking g = 10m/s²]

=> m = 4.57 kg

* acceleration (a) = 1.50m/s²

Substitute these values into equation (ii) as follows;

- 45.7 + T = 4.57 x 1.50

- 45.7 + T = 6.855

Solve for T;

T = 6.855 + 45.7

T = 52.555 N

Therefore, the tension in the rope is 52.555 N