Explanatory comments are added in blue italics.
Problem: A firefighter slides down the fire pole. The weight of the firefighter is 712 N, and her acceleration is 3.00 m/s². What upward force does the pole exert on her?
Step 1. Draw a picture
A picture is drawn showing the directions of the acceleration and velocity.
Step 2. Choose the positive direction and write the givens and the goal
We choose the positive axis downward in the direction of the acceleration, so the acceleration will be a positive number.
+y
Step 3. List the givens and the goal
Given
mg = 712 N
a = 3.00 m/s²
Goal
Find the upward force exerted by the pole on the firefighter.
Step 4. Draw a force diagram
The positive direction is indicated. Two forces act on the firefighter, who is represented by a dot. The weight, mg, is the force of the Earth on the firefighter. The tension, T, is the force of the pole on the firefighter. Note that we only include forces that act on the object of interest.
Forces on the firefighter
Step 5. Write the net force equation
Only one net force equation is needed, since this is a 1-dimensional problem. W and T in the equation represent magnitudes. Therefore, a negative sign is explicitly inserted to indicate that the tension force is in the negative direction.
Fnet = mg - T
Step 6. Apply Newton's 2nd Law
ma is substituted for Fnet.
ma = mg - T
Step 7. Solve algebraically
T is solved for. No numbers have yet been substituted.
T = mg - ma
Step 8. Substitute and reduce
Numerical values with units are substituted, and the equation is reduced. (For the mass, we substitute the quotient of the weight and g.) The result is the magnitude of the tension force.
T = 712 N – (712 N/9.8 m/s²)(3.00 m/s²)
= 494 N
Step 9. Check your answer
The units of the second term on the right reduce to newtons as expected. The sign of T is positive. We expected that, since we set the problem up so that T represented a magnitude.
The value of the tension force is less than the weight. If it were greater than the weight, the firefighter would be accelerating up the pole.
© North Carolina School of Science and Mathematics, All Rights Reserved. These materials may not be reproduced without permission of NCSSM.