a box of mass 10kg is pulled along a rough floor with a force of 100N. the fricyional force acting on the box is a constant 20N. what is the change in the kinetic energy of the box?
To find the change in kinetic energy of the box, we need to calculate the work done on the box. The work done can be determined using the formula:
Work = Force × Distance
In this case, the force applied is 100N, and we need to find the distance. We know that the frictional force is a constant 20N.
The work done against friction can be calculated using the formula:
Work = Force × Distance
Since the frictional force acts against the motion, the work done against friction is negative:
Work against friction = -20N × Distance
The net force acting on the box is the difference between the applied force and the frictional force:
Net Force = Force applied - Force of friction
Net Force = 100N - 20N
Net Force = 80N
Now, we can calculate the distance using the formula:
Net Force = Mass × Acceleration
Acceleration can be calculated using the formula:
Acceleration = Net Force / Mass
Acceleration = 80N / 10kg
Acceleration = 8 m/s^2
Next, we can calculate the distance using the equation of motion:
Distance = (Initial velocity × Time) + (0.5 × Acceleration × Time^2)
Since the box starts from rest (initial velocity = 0) and we are not given the time, we can assume that the box reaches a constant speed. Therefore, we can use the formula:
Distance = 0.5 × (Final velocity^2 - Initial velocity^2) / Acceleration
Since the box is pulled along a rough floor, we assume it reaches a constant speed. Therefore, the final velocity is also zero.
Distance = 0.5 × (0 - 0^2) / 8
Distance = 0
The distance covered is zero because the box didn't move due to the balancing forces.
Now we can calculate the work done:
Work = Force × Distance
Work = 100N × 0
Work = 0J
Since the work done is zero, there is no change in kinetic energy.
To calculate the change in kinetic energy of the box, we need to consider the work done on the box. Work is defined as the force applied to an object multiplied by the distance over which the force is applied. In this case, the work done is equal to the product of the force applied and the distance moved by the box.
The force applied to the box is given as 100N, and the distance moved by the box is not provided in the question. However, based on the given information, we can find the distance moved by dividing the force applied by the net force.
The net force can be calculated by subtracting the frictional force from the applied force. In this case, the frictional force is a constant 20N. Therefore, the net force can be determined as:
Net force = Applied force - Frictional force
Net force = 100N - 20N
Net force = 80N
Now, we need to find the distance moved. We can use the formula:
Work = Force x Distance
Since we're looking for the change in kinetic energy, we know that the work done is equal to the change in kinetic energy. Thus:
Change in kinetic energy = Work = Force x Distance
Plugging in the values we've calculated, we get:
Change in kinetic energy = 80N x Distance
Since the distance moved is not provided, we cannot determine the exact change in kinetic energy without that information.