A student applies a force of magnitude 39.0 N at an angle of 22.6o with the horizontal to push a
4.00-kg textbook 1.00 m across a table from rest to a final speed of 1.75 m/s. Find the work
done by friction on the textbook.
workapplied=39cosine22.6*1m=
work doneonbook= 1/2* 4 *1.75^2
work friction= work applied-work done
39 cos22.6*(1 meter) is the work done by the force, in joules. Subtract the final kinetic energy from that. That will be the work done against friction.
The work done. BY friction is negative
To find the work done by friction on the textbook, we need to calculate the work done by the applied force and subtract the work done by the force of friction.
First, let's calculate the work done by the applied force. We can use the formula:
Work = Force * Distance * cos(theta)
Where:
Force = 39.0 N (magnitude of the applied force)
Distance = 1.00 m (distance the textbook is pushed)
theta = 22.6 degrees (angle of the applied force with the horizontal)
Calculating the work done by the applied force:
Work = 39.0 N * 1.00 m * cos(22.6 degrees)
Work = 33.169 J
Now, let's calculate the work done by the force of friction. The work done by friction is given by the formula:
Work (friction) = Force (friction) * Distance
To find the force of friction, we can use Newton's second law:
Force (friction) = mass * acceleration
The acceleration can be found using the equation for linear motion:
final velocity^2 = initial velocity^2 + 2 * acceleration * distance
Where:
mass = 4.00 kg (mass of the textbook)
initial velocity = 0 m/s (since the textbook is at rest)
final velocity = 1.75 m/s
distance = 1.00 m (distance the textbook is pushed)
Rearranging the equation for acceleration, we get:
acceleration = (final velocity^2 - initial velocity^2) / (2 * distance)
Calculating the acceleration:
acceleration = (1.75 m/s)^2 - (0 m/s)^2 / (2 * 1.00 m)
acceleration = 1.53125 m/s^2
Now, let's calculate the force of friction:
Force (friction) = mass * acceleration
Force (friction) = 4.00 kg * 1.53125 m/s^2
Force (friction) = 6.125 N
Finally, let's calculate the work done by friction:
Work (friction) = Force (friction) * Distance
Work (friction) = 6.125 N * 1.00 m
Work (friction) = 6.125 J
Now, to find the work done by friction on the textbook, we subtract the work done by the applied force from the work done by friction:
Work (done by friction on the textbook) = Work (friction) - Work (applied force)
Work (done by friction on the textbook) = 6.125 J - 33.169 J
Work (done by friction on the textbook) = -27.44 J
Therefore, the work done by friction on the textbook is -27.44 J. The negative sign indicates that the force of friction is opposing the direction of motion.