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Two trolleys A and B of mass 3.2 kg and 2.6 kg respectively are held at rest on a straight horizontal, frictionless track, with a compressed spring between them, as shown in the diagram below - NSC Physical Sciences - Question 4 - 2024 - Paper 1
Question 4
Two trolleys A and B of mass 3.2 kg and 2.6 kg respectively are held at rest on a straight horizontal, frictionless track, with a compressed spring between them, as ... show full transcript
Worked Solution & Example Answer:Two trolleys A and B of mass 3.2 kg and 2.6 kg respectively are held at rest on a straight horizontal, frictionless track, with a compressed spring between them, as shown in the diagram below - NSC Physical Sciences - Question 4 - 2024 - Paper 1
Step 1
Step 2
Calculate the distance travelled by trolley B in 1.3 s.
Answer
To calculate the distance travelled by trolley B, we can use the formula:
Given that trolley A moves with a constant velocity of 0.4 m s^-1 to the left, we need to determine the velocity of trolley B. According to the information provided, the time taken for trolley B to reach the end of the track is 1.3 s, and we can express the distance for trolley B as:
From the conservation of momentum, we have:
Solving this gives:
v_B = rac{3.2 imes 0.4}{2.6} = 0.4923 ext{ m s}^{-1}Thus, the distance:
Step 3
Calculate the time it took the spring to extend to its natural length.
Answer
The average force exerted by the spring on each trolley is given as 4.2 N. Using Newton's second law of motion, we can express the relationship as:
For trolley A:
4.2 = 3.2 imes a_A \ \text{Thus, } a_A = rac{4.2}{3.2} = 1.3125 ext{ m s}^{-2}Now, using the kinematic equations, we have:
v = u + at \ v = 0 ext{ (initial velocity)} + (1.3125 imes t)\ ext{Using the final velocity from previous calculations,}\ 0.49 = 0 + (1.3125 imes t)\ t = rac{0.49}{1.3125} = 0.37 ext{ s}Step 4
How does the magnitude of the velocity of trolley B after the spring has fallen to the track? Write only GREATER THAN, LESS THAN or EQUAL TO. Explain the answer.
Answer
The magnitude of the velocity of trolley B after the spring has fallen to the track will be LESS THAN the velocity of trolley A after the spring has extended because trolley C, which has a larger mass, is now present in the system. The larger mass will result in a smaller acceleration for trolley C after the same force acts upon it, thus reducing the final velocity of trolley B after the spring is released.