Question

A firefighter has mass m; they hear the fire alarm and slides down the pole with acceleration a (which is less than g in magnitude). (a) Write an equation giving the vertical force they must apply to the pole. (b) If their mass is 90.0 kg and they accelerate at 5.00m/s2, what is the magnitude of their applied force?

a) ( F = mg - ma ); 441 N
b) ( F = mg + ma ); 441 N
c) ( F = ma - mg ); 441 N
d) ( F = ma + mg ); 441 N

Answer 1

The correct equation for the force a firefighter must apply to a pole when sliding down is F = mg - ma. For a firefighter with a mass of 90.0 kg and an acceleration of 5.00 m/s², the magnitude of the applied force is 432 N, which is not among the provided options.

Step-by-step explanation:

The question relates to Newton's second law of motion, which involves calculating the vertical force a firefighter must apply to a pole while sliding down with a particular acceleration. According to Newton's second law, Force (F) = mass (m) × acceleration (a). However, when the acceleration is in the direction opposite to the gravitational pull, the net force is the difference between gravitational force (mg) and the force due to acceleration (ma), so the correct equation for this scenario is F = mg - ma.

Given that the mass of the firefighter is 90.0 kg and the acceleration is 5.00 m/s², we can use the equation F = mg - ma to calculate the magnitude of the applied force:

F = m(g - a) = 90.0 kg (9.80 m/s² - 5.00 m/s²) = 90.0 kg × 4.80 m/s² = 432 N

Therefore, the correct option is not listed in the given choices since none matches the calculated force of 432 N.