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An object is acted on by three simultaneous forces: →F1=(−3.00i+2.00j)N, →F2=(6.00i−4.00j)N, and →F3=(2.00i+5.00j)N. The object experiences acceleration of 4.23m/s².

Find the acceleration vector in terms of m.
a) 4.23i+4.23jm/s²
b) −4.23i−4.23j m/s²
c) 4.23i−4.23jm/s²
d) −4.23i+4.23jm/s²

User Ttyyll
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1 Answer

3 votes

Final answer:

The acceleration vector a has components (5/8) * 4.23i + (3/8) * 4.23j, in the same direction as the net force since the acceleration is 4.23 m/s². The mass can be determined using the magnitude of the net force and the provided acceleration magnitude.

Step-by-step explanation:

An object is subject to three simultaneous forces: F1, F2, and F3. The net force acting on the object can be found by summing up these forces vectorially. Once we have the net force represented as a vector, we can then use Newton's second law of motion to find the acceleration vector and the mass of the object.

F1 = (-3.00i + 2.00j) N

F2 = (6.00i - 4.00j) N

F3 = (2.00i + 5.00j) N

The net force Fnet can be calculated as:

Fnet = F1 + F2 + F3

By summing the i and j components separately, we get:

Fnet = (-3 + 6 + 2)i + (2 - 4 + 5)j = (5i + 3j) N

Using Fnet = m * a where 'a' is the acceleration and 'm' is the mass, and given that the acceleration magnitude is 4.23 m/s2, we can find the acceleration vector and the mass of the object. Since the net force has both i and j components, the acceleration vector must have the same direction as the net force vector.

The acceleration vector a will have components such that their ratio matches the ratio of the components of Fnet, hence a = (5/8) * 4.23i + (3/8) * 4.23j.

The mass can be found using the magnitude of the net force and the acceleration:

|Fnet| = m * |a|

The speed of the object after 5.00 s, assuming it starts from rest, can be found using the formula v = a * t, where 'v' is the velocity, 'a' is the acceleration, and 't' is time. The velocity's components after 5.00 s can also be calculated using the same acceleration vector.

User AabidMulani
by
8.2k points
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