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Figure 8 shows a model of a system being designed to move concrete building blocks from an upper to a lower level - AQA - A-Level Physics - Question 6 - 2017 - Paper 1
Question 6
Figure 8 shows a model of a system being designed to move concrete building blocks from an upper to a lower level. The model consists of two identical trolleys of m... show full transcript
Worked Solution & Example Answer:Figure 8 shows a model of a system being designed to move concrete building blocks from an upper to a lower level - AQA - A-Level Physics - Question 6 - 2017 - Paper 1
Step 1
The tension in the wire when the trolleys are moving is T.
Answer
To represent the forces acting on trolley A, draw the following arrows:
- An arrow downwards labeled as weight, pointing to the center of the trolley, representing the gravitational force (Mg).
- An arrow parallel to the slope of the ramp, labeled as tension, pointing up the ramp (T).
- An arrow perpendicular to the ramp, showing the normal force (N) acting on the trolley.
Step 2
Show that the acceleration a of trolley B along the ramp is given by a = mg sin 35° / (M + m)
Answer
By applying Newton’s second law:
- For trolley A:
- The forces along the ramp are: T - mg sin 35° = Ma
- For trolley B:
- The forces along the ramp are: mg sin 35° - T = ma
Adding these two equations gives: Thus, simplifying yields:
Step 3
Compare the momentum of loaded trolley A as it moves downwards with the momentum of loaded trolley B.
Answer
The momentum of an object is given by the product of its mass and velocity. Let:
- The mass of loaded trolley A be (M + 2m), and its downward velocity be v.
- The mass of loaded trolley B be M, and its upward velocity also be v.
Therefore, the momentum of trolley A is: And the momentum of trolley B is: Here, is greater than since .
Step 4
Step 5
Calculate the number of blocks that can be transferred to the lower level in 30 minutes.
Answer
If each journey takes T seconds, the number of journeys in 30 minutes (1800 seconds) is: And if unblocking and reloading takes 12 seconds per operation, the total number of blocks transferred can be calculated by: