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 s² 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 Newtons Second Law: 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 determine the tension $T$ in the rope AB, we consider the forces acting on the system (scale pan + brick).

Identify the mass and acceleration: The total mass of the system is $M = m_{pan} + m_{brick} = 0.5 ext{ kg} + 1.5 ext{ kg} = 2.0 ext{ kg}$ The system is accelerated upward with $a = 0.5 ext{ m/s}^2$ .
Apply Newton's second law: We can write the equation of motion as: $T - M imes g = M imes a$ Here, $g$ is the acceleration due to gravity (approximately $9.81 ext{ m/s}^2$ ). Therefore: $T - 2.0 imes 9.81 = 2.0 imes 0.5$ $T - 19.62 = 1.0$ $T = 20.62 ext{ N}$ Thus, the tension in the rope AB is approximately $20.6 ext{ N}$ .

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 can analyze the forces acting on just the brick:

Consider the forces on the brick: The upward tension $T$ and the downward weight of the brick. The weight of the brick is: $W_{brick} = m_{brick} imes g = 1.5 ext{ kg} imes 9.81 ext{ m/s}^2 = 14.715 ext{ N}$
Apply Newton's second law to the brick: $T - W_{brick} = m_{brick} imes a$ Substitute for tension: $T - 14.715 = 1.5 imes 0.5$ Thus, $T - 14.715 = 0.75$ Therefore, $T = 15.465 ext{ N}$ So, the magnitude of the force exerted on the scale pan by the brick is approximately $15.5 ext{ N}$ .

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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