A-Level Edexcel Maths Mechanics Newtons Second Law: A particle P of mass 0.4 kg is m

A particle P of mass 0.4 kg is moving under the action of a constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 3 - 2003 - Paper 1

Question 3

A particle P of mass 0.4 kg is moving under the action of a constant force F newtons. Initially the velocity of P is (6i - 2j) m s$^{-1}$ and 4 s later the velocity ... show full transcript

Worked Solution & Example Answer:A particle P of mass 0.4 kg is moving under the action of a constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 3 - 2003 - Paper 1

Step 1

Find, in terms of i and j, the acceleration of P.

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Answer

To find the acceleration of particle P, we will use the formula:

ext{acceleration} = rac{ ext{change in velocity}}{ ext{time}}

The change in velocity, ( riangle v ), over 4 seconds is:

\triangle v = v_f - v_i = (-4i + 2j) - (6i - 2j)

Calculating this gives:

\triangle v = (-4i + 2j - 6i + 2j) = (-10i + 4j)

Thus, the acceleration is:

a = \frac{\triangle v}{t} = \frac{(-10i + 4j)}{4} = - rac{5}{2}i + j

So, the acceleration of P is:

a = -5i + 12j ext{ m s}^{-2}$$

Step 2

Calculate the magnitude of F.

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Answer

To calculate the magnitude of the force F acting on particle P, we will use Newton's second law of motion:

F = ma

Here, the mass ( m = 0.4 , ext{kg} ) and we need to find the magnitude of acceleration, which we found in part (a):

|a| = \sqrt{\left(-\frac{5}{2}\right)^2 + (1)^2} = \sqrt{\frac{25}{4} + 1} = \sqrt{\frac{25}{4} + \frac{4}{4}} = \sqrt{\frac{29}{4}} = \frac{\sqrt{29}}{2}

Substituting back into Newton's law:

|F| = 0.4 \times \left(\frac{\sqrt{29}}{2}\right) = \frac{0.4\sqrt{29}}{2} = 0.2\sqrt{29} ext{ N}

Thus, the magnitude of F, utilizing ( a = \sqrt{(2)^2 + (4.8)^2} = 5.2 \text{ N} ).

A particle P of mass 0.4 kg is moving under the action of a constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 3 - 2003 - Paper 1

Worked Solution & Example Answer:A particle P of mass 0.4 kg is moving under the action of a constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 3 - 2003 - Paper 1

Find, in terms of i and j, the acceleration of P.

Calculate the magnitude of F.

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