An engine force of 1000 N is required to move a cart of mass 2 metric tons slowly with constant speed on a rough horizontal road. Determine the force required to move the same cart with an acceleration of 1 m/s² on the same road.

1500 N

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1000 N

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2000 N

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3000 N

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Solution

The correct option is D 3000 N
The net force on a body moving at a constant velocity is zero. The engine and the cart are moving on a rough surface. Therefore, the forward force must be equal to the opposing frictional force, i.e.,
$f_{e n g i n e + c a r t}$ (frictional force acting on engine and cart) = 1000 N
The net force to move the cart with an acceleration of 1 m/s²:
$F_{n e t}$ = 2000 ✖ 1 = 2000 N
Thus, the force required to pull the cart (F) is,
$F_{n e t}$ = F - $f_{e n g i n e + c a r t}$ ⇒ 2000 = F - 1000
⇒ F = 3000 N

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