A vertical rope AB has its end B attached to the top of a scale pan. The scale pan has mass 0.5 kg and carries a brick of mass 1.5 kg, as shown in Figure 1. The scale pan is raised vertically upwards with constant acceleration 0.5 m s−2 using the rope AB. The rope is modelled as a light inextensible string. (a) Find the tension in the rope AB. (b) Find the magnitude of the force exerted on the scale pan by the brick.

A-Level Edexcel Maths Mechanics Forces: A vertical rope AB has its end B

A vertical rope AB has its end B attached to the top of a scale pan - Edexcel - A-Level Maths Mechanics - Question 2 - 2016 - Paper 1

Question 2

A vertical rope AB has its end B attached to the top of a scale pan. The scale pan has mass 0.5 kg and carries a brick of mass 1.5 kg, as shown in Figure 1. The scal... show full transcript

Worked Solution & Example Answer:A vertical rope AB has its end B attached to the top of a scale pan - Edexcel - A-Level Maths Mechanics - Question 2 - 2016 - Paper 1

Step 1

Find the tension in the rope AB.

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Answer

To find the tension $T$ in the rope AB, we start by analyzing the forces acting on the entire system.

The forces acting on the entire system (scale pan and brick) are:

The gravitational force acting downwards due to the mass of the scale pan ( extit{m}_1 = 0.5 kg) and the brick ( extit{m}_2 = 1.5 kg).
The tension $T$ acting upwards against the gravity.

Using Newton's second law, we set up the equation: $T - (m_1 + m_2)g = (m_1 + m_2)a$ Where:

$g$ is the acceleration due to gravity (approximately $9.81 ext{ m/s}^2$ ),
$a$ is the upward acceleration ( $0.5 ext{ m/s}^2$ ).

Substituting the values: $T - (0.5 + 1.5)(9.81) = (0.5 + 1.5)(0.5)$ $T - 19.62 = 1$ $T = 20.62 ext{ N}$

Thus, the tension in the rope AB is approximately $20.6$ N.

Step 2

Find the magnitude of the force exerted on the scale pan by the brick.

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Answer

To find the force exerted on the scale pan by the brick, we consider the forces acting specifically on the brick itself:

The gravitational force acting downwards on the brick is given by: $F_{gravity} = m_2g = 1.5 imes 9.81$
The tension $T$ from the rope acts upwards.

Using Newton's second law for the brick: $T - m_2g = m_2a$

Substituting the known values: $T - 1.5 imes 9.81 = 1.5 imes 0.5$ $T - 14.715 = 0.75$ $T = 15.465 ext{ N}$

Thus, the magnitude of the force exerted on the scale pan by the brick is approximately $15.5$ N.

A vertical rope AB has its end B attached to the top of a scale pan - Edexcel - A-Level Maths Mechanics - Question 2 - 2016 - Paper 1

Worked Solution & Example Answer:A vertical rope AB has its end B attached to the top of a scale pan - Edexcel - A-Level Maths Mechanics - Question 2 - 2016 - Paper 1

Find the tension in the rope AB.

Find the magnitude of the force exerted on the scale pan by the brick.

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