A 25.0 kg pickle is accelerated from rest through a distance of 6.0 m in 4.0 s across a
level floor. If the friction force between the pickle and the floor is 3.8 N, what is the
work done to move the object?
Add the KE increase and the work done against friction.
The final velocity is twice the average, or 3.0 m/s
The final KE is (1/2)*25*3^2 = 112.5 J
The friction work done is 6*3.8 = 22.8 J
To find the work done to move the object, we need to calculate the net force acting on the pickle and then use the equation for work.
The net force on an object can be calculated using Newton's second law:
net force = mass * acceleration
In this case, since the pickle starts from rest and is accelerated across a level floor, the net force is the force applied to the pickle minus the friction force:
net force = force applied - friction force
The work done on an object is given by the equation:
work = force * distance
To calculate the work done, we need to find the force applied to the pickle. We can do this by rearranging the equation for net force:
net force = mass * acceleration
Applying it to our problem:
net force = 25.0 kg * acceleration
We know that the pickle travels a distance of 6.0 m in 4.0 s, so we can calculate the acceleration using the equation of motion:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the pickle starts from rest, the initial velocity is 0, and the equation simplifies to:
distance = 0.5 * acceleration * time^2
Rearranging the equation:
acceleration = (2 * distance) / (time^2)
Substituting the values:
acceleration = (2 * 6.0 m) / (4.0 s)^2
acceleration = (12.0 m) / (16.0 s^2)
acceleration = 0.75 m/s^2
Now we can calculate the net force:
net force = 25.0 kg * 0.75 m/s^2
net force = 18.75 N
Finally, we can calculate the work done:
work = (net force - friction force) * distance
work = (18.75 N - 3.8 N) * 6.0 m
work = 14.95 N * m
Therefore, the work done to move the object is 14.95 Joules.