The figure above shows the net force exerted on an object as a function of the position of the object. The object starts from rest at position x = 0 m and acquires a speed of 3.0 m / s after traveling the distance of 0.090 m shown above. What is the mass of the object?

0.06 Kg

Explanation:

From the question given above, the following data were obtained:

Initial velocity (u) = 0 m/s

Final velocity (v) = 3.0 m/s

Distance (s) = 0.09 m

Net Force (F) = 3 N

Mass (m) =?

Next, we shall determine the acceleration of the object. This can be obtained as follow:

Initial velocity (u) = 0 m/s

Final velocity (v) = 3.0 m/s

Distance (s) = 0.09 m

Acceleration (a) =?

v² = u² + 2as

3² = 0² + (2 × a × 0.09)

9 = 0 + 0.18a

9 = 0.18a

Divide both side by 0.18

a = 9 / 0.18

a = 50 m/s²

Finally, we shall determine the mass of the object. This can be obtained as follow:

Net Force (F) = 3 N

Acceleration (a) = 50 N

Mass (m) =?

F = ma

3 = m × 50

Divide both side by 50

m = 3 / 50

m = 0.06 Kg

Therefore, the mass of the object is 0.06 Kg

The required value for the mass of object is 0.06 kg.

Given data:

The speed of object is, v = 3.0 m/s.

The distance travelled by object is, s = 0.090 m.

From the given graph in the question, we obtain the following details as,

The net force applied on the object is, .

The initial velocity is, u = 0 m/s.

Now using the third kinematic equation of motion to obtain the acceleration of object as,

v² = u² + 2as

3² = 0² + (2 × a × 0.09)

9 = 0 + 0.18a

9 = 0.18a

Solving as,

a = 9 / 0.18

a = 50 m/s²

Now, as per the Newton's second law of motion, we have the expression for the applied force as,

Here, m is the mass of object.

Solving as,

Thus, we can conclude that the required value for the mass of object is 0.06 kg.

Learn more about the Newton's second law here:

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