# Tension force and Newton's third law

When a horse pulls a cart, suppose connected by a string, it produces a tension $$T$$ in the string. The cart in turn pulls the horse by an equal force $$T$$ in the opposite direction. If this T>f, the friction on the cart, it moves forward. But how does the horse move with the cart pulling it? From what i have understood the horse presses the ground in an inclined direction and the horizontal component of the corresponding reaction is the force with which it pulls the cart i.e the tension T. So the more effort it puts, the same magnitude of force will pull it back. I do have the intuition for Newton's third law, that action and reaction are on different objects, for eg incase of a gun firing a bullet, the bullet exerts the same force to the gun, but the gun is much heavier so it can only nudge the gun a bit in the opposite direction. It makes sense. But I'm having a bit of an issue with tension. Can anyone please elaborate?

• " the horse presses the ground in an inclined direction and the horizontal component of the corresponding reaction is the force with which it pulls the cart i.e the tension T" If you mean that the magnitude of the reaction force is equal to the tension if they are moving at constant velocity, then yes, that's true. If you mean that the reaction force is the tension force, then no. Jun 18, 2021 at 14:06
• i'm saying, the Tension force is because of the reaction
– rdev
Jun 18, 2021 at 15:00

The two forces in Newton's third law are on different things ($$F_1$$ on mass $$m_1$$, $$F_2$$ on mass $$m_2$$ ) and each responds by moving $$F_1=m_1a_1$$ and $$F_2=m_2a_2$$ due to the force on it without regard to what the other object is doing. In the abence of any any other forces (not the case with the horse + cart as there is friction) we have $$0=F_1+F_2= \frac d{dt}(m_1v_1+m_2v_2),$$
You have to focus just on the forces on the cart to decide if it'll move. If the force $$T$$ on the cart is greater than the friction force resisting the cart, then it'll accelerate in the direction of $$T$$.