Two carts, A and B, are initially at rest on frictionless, horizontal table. A c

Question

Two carts, A and B, are initially at rest on frictionless, horizontal table. A constant force of magnitude F_o is exerted on each can as it travels from the First mark on the table to the second, after which each cart glides freely The mass of cart A is less than that of cart B. Is the magnitude of the acceleration of cart A greater than, less than, or equal to the magnitude of the acceleration of cart B while the carts are between the two marks? Explain. Is the kinetic energy of cart A greater than, less than, or equal to the kinetic energy of cart B after the carts have passed the second mark? Explain. Is the magnitude of the momentum of can A greater than, less than, or equal to the magnitude the momentum of cart B after the carts have passed the second mark? Explain.

Explanation / Answer

1) We have, F = m*a

Since mb> ma and F is same for both masses

=> acceleration for ma is greater

we have V^2 = U^2 +2*a*s   [law of motion]

U = 0 for both, s is same for both

=> if velocity of a will be higher since its acceleration is higher.

2)Work done by force to displace a object by d distance in its direction is given as

W = Fd

using this, since both forces are same and distance covered are also same => Wa = Wb

now the work done on each body is transformed into its kinetic energy

=> kinetic energy of both the blocks will be same at the mark

3) Kinetic energy of an object is = 0.5*mv^2

momentum, p = mv

=> KE = 0.5*p*v

since KE for both the blocks is same

=> 0.5*pa*va = 0.5*pb*vb

also we know va>vb

=>pa<pb

hence momentum of block b is greater than that of a

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