A vertical light rod PQ has a particle of mass 0.5 kg attached to it at P and a particle of mass 0.75 kg attached to it at Q, to form a system, as shown in Figure 2. The system is accelerated vertically upwards by a vertical force of magnitude 15 N applied to the particle at Q. Find the thrust in the rod.

A-Level Edexcel Maths Mechanics Newtons Second Law: A vertical light rod PQ has a pa

A vertical light rod PQ has a particle of mass 0.5 kg attached to it at P and a particle of mass 0.75 kg attached to it at Q, to form a system, as shown in Figure 2 - Edexcel - A-Level Maths Mechanics - Question 5 - 2017 - Paper 1

Question 5

A vertical light rod PQ has a particle of mass 0.5 kg attached to it at P and a particle of mass 0.75 kg attached to it at Q, to form a system, as shown in Figure 2.... show full transcript

Worked Solution & Example Answer:A vertical light rod PQ has a particle of mass 0.5 kg attached to it at P and a particle of mass 0.75 kg attached to it at Q, to form a system, as shown in Figure 2 - Edexcel - A-Level Maths Mechanics - Question 5 - 2017 - Paper 1

Step 1

For mass at P: Find thrust (T)

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Answer

Using Newton's second law for the mass at P: $T - 0.5g = 0.5a$ Substituting $g = 9.8 \, ext{m/s}^2$ : $T - 0.5 \times 9.8 = 0.5a$ This simplifies to: $T = 0.5a + 4.9$

Step 2

For mass at Q: Find net force and acceleration

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Answer

Using Newton's second law for the mass at Q: $F_{net} = 15 - T - 0.75g$ This gives: $15 - T - 0.75 \times 9.8 = 0.75a$ Substituting $g = 9.8 \, ext{m/s}^2$ : $15 - T - 7.35 = 0.75a$ This simplifies to: $7.65 - T = 0.75a$ Now, we have two equations to solve for T and a.

Step 3

Solve the equations

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Answer

We can use substitution from the first equation into the second: From the first equation, express $a$ in terms of $T$ : $a = \frac{T - 4.9}{0.5}$ Substituting this in the second equation yields: $7.65 - T = 0.75 \left(\frac{T - 4.9}{0.5} \right)$ This now simplifies and gives us a single equation in terms of T. Solving for T leads us to: $T = 6 \text{ N}$

A vertical light rod PQ has a particle of mass 0.5 kg attached to it at P and a particle of mass 0.75 kg attached to it at Q, to form a system, as shown in Figure 2 - Edexcel - A-Level Maths Mechanics - Question 5 - 2017 - Paper 1

Worked Solution & Example Answer:A vertical light rod PQ has a particle of mass 0.5 kg attached to it at P and a particle of mass 0.75 kg attached to it at Q, to form a system, as shown in Figure 2 - Edexcel - A-Level Maths Mechanics - Question 5 - 2017 - Paper 1

For mass at P: Find thrust (T)

For mass at Q: Find net force and acceleration

Solve the equations

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