Question

I did an experiment in which a cart on wheels is getting pulled by a pulley hanging off the surface. The pulley has a 50g hanger which causes the motion. The cart is 300g and then in different trials added one 50g weight, two, three, and then four. The slope was 0 degrees. My question is: Describe (and show with pictures) what forces change for each of the different configurations used.

Answer 1

let m be the mass of cart and M be the mass of hanger and added mass (total mass M).

Figure shows the different forces acting on hanger and cart.

Force Mg is due to weight of hanger and added masses. T is the Tension force acting throughout the string. Force mg is due to weight of Cart and N are the normal reaction force from contact surface. Let us assume, cotact surface for cart is smooth and friction force is negligible.

By applying Newton's law to the hanger, we get,

Mg - T = M a .............. (1)

By applying Newton's law to the cart, we get,

From above , we get Tension force as , T = m a   ................(2)

if we add (1) and (2) , Mg = ( M + m ) a

hence acceleration, a = [ M / (M+m) ] g ..................(3)

By substituting acceleration in eqn.(2), we get tension force T as

T = [ ( M m ) / (M+m) ] g ..................(4)

In the above equation, mass of cart m is constant, but due to added mass M is changing.

Hence Tension force , which is pulling the cart , is changing according to equation (4)