Question

Daisy is walking across a force platform, and the forces exerted by her foot during a step are recorded. The peak vertical reaction force is 1200 N (this force acts upward on Daisy). At the same instance the braking force is 200 N (this force acts backward on Daisy). How large and in what direction is the resultant force?

a. 1400 N, 90 degrees
b. 1300.4 N, 170.5 degrees
c. 1216.6 N 99.5 degrees
d. 1015.6 N, 110.8 degrees

Answer 1

The correct answer is (c) 1216.6 N at 99.5 degrees. The magnitude of the resultant force is calculated using the Pythagorean theorem, and the direction is determined by the angle from the vertical, considering the forces are perpendicular to each other.

Step-by-step explanation:

When Daisy is walking across a force platform, two forces are acting on her: a peak vertical reaction force of 1200 N, which acts upwards, and a braking force of 200 N, which acts backward. The resultant force can be calculated using the Pythagorean theorem because the forces are perpendicular to each other. The magnitude of the resultant force (R) is given by:

R = √(Fvertical^2 + Fbraking^2) = √(1200^2 + 200^2) = √(1440000 + 40000) = √1480000 ≈ 1216.6 N

The direction of the resultant force can be calculated by finding the angle (θ) with respect to the vertical using the tangent function:

θ = arctan(Fbraking / Fvertical) = arctan(200 / 1200) ≈ arctan(0.1667) ≈ 9.46 degrees from the vertical, which is equivalent to 90 + 9.46 = 99.46 degrees from the horizontal. Rounding the angle to one decimal place, we have 9.5 degrees from vertical or 99.5 degrees from horizontal.

Thus, the correct answer is (c) 1216.6 N at 99.5 degrees.