The cart has a mass of 2.3kg and is attached to a 1.7kg object via a rope. Assuming there is no friction, calculate the magnitude of the force of tension in the rope.

Answer 1

To calculate the magnitude of the force of tension in the rope, we need to consider that the force of tension is equal to the force applied to an object in order to accelerate it. In this case, the force of tension will be equal to the force applied to accelerate the cart and the object.

Let's assume that the force of tension is T in Newtons.

According to Newton's second law of motion, the force applied to an object is equal to its mass multiplied by its acceleration: F = m * a.

The force applied to the cart can be calculated by: F1 = m1 * a1, where m1 is the mass of the cart and a1 is its acceleration. Similarly, the force applied to the object can be calculated by: F2 = m2 * a2, where m2 is the mass of the object and a2 is its acceleration.

In this case, the two forces are equal because they are connected by the same rope, so we can write: F1 = F2.

Using the formula F = m * a, we can rewrite this as:

m1 * a1 = m2 * a2.

To find the acceleration, we can use the formula a = F / m, where F is the force applied and m is the mass.

So, we have:

a1 = T / m1 and a2 = T / m2.

Substituting these into the equation m1 * a1 = m2 * a2, we get:

m1 * (T / m1) = m2 * (T / m2).

Simplifying, we find:

T = T.

This equation tells us that the magnitude of the force of tension in the rope is equal to T, which means the force of tension is T = T.