Question

A 16.3 lb object has the acceleration components (0.35 m/s^2) and (0.79 m/s^3). What is the magnitude of the net force acting on the object at time t = 4.07 s? a) Missing context, no question. b) Calculate the magnitude of the net force. c) Determine the direction of the net force. d) Explain the significance of the given acceleration components

Answer 1

To find the magnitude of the net force acting on the object, we need to calculate the total acceleration by adding the two components of acceleration. Then, multiply the total acceleration by the mass of the object to get the net force. The net force is approximately 3.99 N.

Step-by-step explanation:

To calculate the magnitude of the net force acting on the object at time t = 4.07 s, we can use Newton's second law, which states that force is equal to mass times acceleration. Given that the object has a mass of 16.3 lb, we need to convert it to kilograms by dividing it by 2.205 (1 kg = 2.205 lb). Hence, the mass of the object is approximately 7.39 kg.

The net force can be found by multiplying the mass by the acceleration, which is given as (0.35 m/s^2) and (0.79 m/s^3). However, since acceleration has different units in each component, we need to convert one of them to match the other. Let's convert the second component to m/s^2 by dividing it by time (t = 4.07 s) twice. The value of the second component is approximately 0.19 m/s^2.

Now, we can calculate the net force by adding the two components of acceleration and multiplying it by the mass:

Fnet = 7.39 kg × (0.35 m/s^2 + 0.19 m/s^2) ≈ 7.39 kg × 0.54 m/s^2 = 3.99 N.

The magnitude of the net force acting on the object at time t = 4.07 s is approximately 3.99 N.

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