Mc Exploration 1.1.b Does the force of the string, Fs, on the hanging mass equal

Question

Mc Exploration 1.1.b Does the force of the string, Fs, on the hanging mass equal the gravitational force on the hanging mass (after release from res)? Explain. Exploration 1.1.c If the hanging m mh, after release from rest is moving, explain the motion in terms of the net force on mb. If your explanation contradicts your answer to part 1.1.b, explain or reconsider your answer to 1.1.b. Exploration 1.1.d If, after the hanging mass, my, is released from rest, the cart is moving, explain in terms of the net force on the cart. Is the net force on the cart greater than, less than or equal to mhg? Explain. Exploration 1.1.e. After the hanging mass, mh, is released from rest, would the cart and the hanging mass move at the same acceleration? Explain. Exploration 1.1.e. Derive an equation for the acceleration of the system of cart plus hanging mass, a, in terms of the mass of the cart, me, and m and g.

Explanation / Answer

1.1.b Yes, Since mh and mc are both interconnected from string, the gravitational force on mh will be also felt by the mc cart but in form of force of string.

1.1.c Net force on mh is due to gravitational pull as well as due to string force fs, which is pulling it upward. This string force fs is moving the cart in rightward direction.

1.1.d/e After the release of mh,

we can write force equation on mh as

mh*g-fs = mh*a; where a is acceleration experienced by it

also, mc*a = fs

=> mh*g-mc*a = mh*a

=> a = g*mh/(mc+mh)

Force experienced by mc is = mc*a = mc*g*mh/(mc+mh) = mh*g*(mc/(mc+mh))

this is less than mh*g

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