A box with mass 4.0 kg is pulled from rest along a horizontal floor by a constant force F. A constant frictional force of 1.0 N acts on the box. When the box has travelled 1.0 m its velocity is 1.5 m / s.The kinetic energy of the box is equal to the work done on the box.What is force F ?
Question
A box with mass 4.0 kg is pulled from rest along a horizontal floor by a constant force F. A constant frictional force of 1.0 N acts on the box. When the box has travelled 1.0 m its velocity is 1.5 m / s.The kinetic energy of the box is equal to the work done on the box.What is force F ?
Solution
To solve this problem, we need to use the work-energy theorem which states that the work done on an object is equal to the change in its kinetic energy.
Step 1: Calculate the final kinetic energy of the box. The kinetic energy (KE) of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity. Substituting the given values, we get KE = 1/2 * 4.0 kg * (1.5 m/s)^2 = 4.5 Joules.
Step 2: Calculate the work done by the frictional force. The work done (W) by a force is given by the formula W = F * d, where F is the force and d is the distance. The work done by the frictional force is W = 1.0 N * 1.0 m = 1.0 Joule.
Step 3: Calculate the total work done on the box. According to the work-energy theorem, the total work done on the box is equal to the change in its kinetic energy, which is 4.5 Joules. But this total work is the sum of the work done by the force F and the work done by the frictional force. Therefore, the work done by the force F is 4.5 Joules - 1.0 Joule = 3.5 Joules.
Step 4: Calculate the force F. Finally, we can find the force F by rearranging the formula for work done: F = W / d. Substituting the values we found, we get F = 3.5 Joules / 1.0 m = 3.5 N.
So, the force F is 3.5 N.
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