A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4sec his displacement relative to the ground will be
Question
A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4sec his displacement relative to the ground will be
Solution
The problem involves the principle of conservation of momentum.
Step 1: Calculate the total initial momentum of the system (man + trolley). Since both are initially at rest, the total initial momentum is 0.
Step 2: When the man starts walking, he imparts a momentum to the trolley in the opposite direction (due to Newton's third law). The man's momentum is his mass times his velocity, which is 80 kg * 1 m/s = 80 kg*m/s.
Step 3: Since the total momentum of the system must remain 0 (conservation of momentum), the trolley moves in the opposite direction with a momentum of -80 kgm/s. We can find the velocity of the trolley by dividing this momentum by the trolley's mass: -80 kgm/s / 320 kg = -0.25 m/s.
Step 4: The man's displacement relative to the ground is the sum of his displacement on the trolley and the trolley's displacement. The man moves 1 m/s * 4 s = 4 m on the trolley, and the trolley moves -0.25 m/s * 4 s = -1 m, so the man's total displacement is 4 m - 1 m = 3 m.
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