A student is attempting to haul a 500 kg log down a 24 degree hill. The log has a coefficient of friction of .5. The student is pulling with about 1700 N of force. Is the student pulling too hard or too lightly? Calculate exactly how much harder or less hard the student should pull the log.
To determine if the student is pulling too hard or too lightly, we need to compare the force applied by the student with the opposing force of friction.
First, let's calculate the force of friction using the formula: friction force = coefficient of friction x normal force.
The normal force is the component of the weight of the log perpendicular to the surface of the hill, which can be calculated using the formula: normal force = mass x gravity x cos(angle of incline).
Given:
Mass of the log (m) = 500 kg
Angle of incline (θ) = 24 degrees
Coefficient of friction (μ) = 0.5
Force applied by the student (F) = 1700 N
Step 1: Calculate the normal force.
normal force = m x g x cos(θ)
normal force = 500 kg x 9.8 m/s^2 x cos(24°)
normal force ≈ 4,350 N
Step 2: Calculate the force of friction.
friction force = μ x normal force
friction force ≈ 0.5 x 4,350 N
friction force ≈ 2,175 N
Now that we have the force of friction, we can compare it with the force applied by the student.
If the force applied by the student is less than the force of friction, the student is pulling too lightly and should pull harder. Conversely, if the force applied by the student is greater than the force of friction, the student is pulling too hard and should pull less.
In this case, the force applied by the student (1700 N) is less than the force of friction (2175 N), indicating that the student is pulling too lightly.
To find out how much harder the student should pull, we need to calculate the difference between the force of friction and the force applied by the student.
Difference = force of friction - force applied by the student
Difference = 2175 N - 1700 N
Difference ≈ 475 N
Therefore, the student should pull approximately 475 N harder to overcome the force of friction and effectively move the log down the hill.