A boa box of mass 10kg is pulled along a rough floor with a force of 100N. the frictional force acting on the box is a constant 20N. What is the change in the kinetic energy of the box?
the box is constantly accelerating
the net force is ... 100 N - 20 N = 80 N
f = m a ... acceleration = force / mass = 80 N / 10 kg = 8 m/s^2
the K.E. is increasing
To find the change in kinetic energy of the box, we need to know the initial and final velocities of the box. However, this information is not provided in the question. We can still determine the work done and infer the change in kinetic energy using the work-kinetic energy theorem.
The work done on an object is given by the equation:
Work = Force * Distance * cos(θ)
Where:
- Force is the applied force on the object (in this case, the pulling force of 100N).
- Distance is the displacement of the object.
- θ is the angle between the direction of the force and the direction of displacement.
The frictional force is acting against the applied force, so the angle between the force and displacement is 180 degrees (or π radians).
Therefore, the work done against friction is given by:
Work against friction = Frictional force * Distance * cos(180°)
Since the cos of 180° is -1:
Work against friction = (-1) * 20N * Distance = -20N * Distance
Similarly, the work done by the applied force is given by:
Work applied force = Applied force * Distance * cos(0°) = 100N * Distance
The net work done on the box is the sum of the work done by the applied force and the work done against friction:
Net work done = Work applied force + Work against friction
Net work done = 100N * Distance - 20N * Distance
Net work done = (100N - 20N) * Distance
Net work done = 80N * Distance
According to the work-kinetic energy theorem, the net work done on an object is equal to the change in kinetic energy:
Net work done = Change in kinetic energy
Therefore, the change in kinetic energy of the box is given by:
Change in kinetic energy = 80N * Distance
Note: Without knowing the distance traveled by the box, we cannot calculate the exact change in kinetic energy.