Question

At t = 18.0 seconds, an object with mass 5.5 kg was observed to have a velocity of <13, 28, -8> m/s. At t = 18.20 seconds, its velocity was <15, 18, 25> m/s. What was the average (vector) net force acting on the object?

(A) <1.5, -5, 33> N
(B) <0.1, -1, 1.35> N
(C) <2, -10, 17.5> N
(D) <0.5, -2, 3> N

Answer 1

The average net force is found by calculating the change in velocity divided by the time interval, and then multiplying by the object's mass. Upon calculation, the result obtained for the average net force, <11, -55, 181.5> N, does not match any of the given options, suggesting a possible error in the provided information or the answer choices.

Step-by-step explanation:

To determine the average net force acting on the object, we must first calculate the change in velocity (Δv) and the time interval (Δt) over which this change occurred. The change in velocity can be found by subtracting the initial velocity vector at t = 18.0 seconds from the final velocity vector at t = 18.20 seconds:

Δv = <15 - 13, 18 - 28, 25 - (-8)> m/s
= <2, -10, 33> m/s

The time interval is Δt = tfinal - tinitial = 18.20 s - 18.00 s = 0.20 seconds.

Now, we apply Newton's second law, F = ma, where a is the acceleration. The acceleration can be calculated using a = Δv / Δt. For an object with a mass of 5.5 kg, we find:

a = <2, -10, 33> m/s / 0.20 s = <10, -50, 165> m/s2

The average force is then:

F = m * a = 5.5 kg * <10, -50, 165> m/s2 = <55, -275, 907.5> N

However, we need to account for the fact that the average force is calculated over the 0.20-second interval. This gives:

Favg = F * Δt = <55, -275, 907.5> N * 0.20 s = <11, -55, 181.5> N

None of the given options (A, B, C, or D) match the calculated average net force of <11, -55, 181.5> N. Thus, it seems there has been an error in calculation or in the provided options. If this is the problem presented, then a reevaluation or clarification of the given data and possible answers would be necessary.