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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Friction

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Friction

Starting from rest, a scooter travels with a constant acceleration...

Starting from rest, a scooter travels with a constant acceleration for a time Δt1\Delta t_1, subsequently moves with a constant velocity for the next Δt2\Delta t_2, and finally undergoes a constant deceleration for the next Δt3\Delta t_3 to come to rest. A 500 N500 \text{ N} man sitting on the scooter behind the driver manages to remain at rest with respect to the scooter without touching any other part. The force exerted by the seat on the man is

Options

  1. A500 N500 \text{ N} throughout the journey
  2. Bless than 500 N500 \text{ N} throughout the journey
  3. C>500 N> 500 \text{ N} for time Δt1\Delta t_1 and Δt3\Delta t_3 and 500 N500 \text{ N} for Δt2\Delta t_2
  4. Dmore than 500 N500 \text{ N} throughout the journey

Correct answer

C. >500 N> 500 \text{ N} for time Δt1\Delta t_1 and Δt3\Delta t_3 and 500 N500 \text{ N} for Δt2\Delta t_2

Step-by-step solution

During the time interval Δt1\Delta t_1, the scooter accelerates with an acceleration a1a_1. The forces acting on the man are his weight W=500 NW = 500 \text{ N} acting downwards and the force from the seat. Since the man is at rest relative to the scooter, he accelerates with a1a_1. The force exerted by the seat has a vertical normal component N=500 NN = 500 \text{ N} to balance gravity and a horizontal frictional component f=ma1f = m a_1 to provide the acceleration.

The total force exerted by the seat is F1=N2+f2=5002+(ma1)2F_1 = \sqrt{N^2 + f^2} = \sqrt{500^2 + (m a_1)^2}, which is greater than 500 N500 \text{ N}.

During the time interval Δt2\Delta t_2, the scooter moves with a constant velocity, so the acceleration is zero. The horizontal force is zero, and the force exerted by the seat is only the vertical normal force N=500 NN = 500 \text{ N}.

During the time interval Δt3\Delta t_3, the scooter decelerates with an acceleration a3a_3. The force exerted by the seat again has a horizontal component f′=ma3f' = m a_3 and a vertical component N=500 NN = 500 \text{ N}. The total force is F3=5002+(ma3)2F_3 = \sqrt{500^2 + (m a_3)^2}, which is greater than 500 N500 \text{ N}.

Thus, the force exerted by the seat on the man is >500 N> 500 \text{ N} for time Δt1\Delta t_1 and Δt3\Delta t_3, and 500 N500 \text{ N} for Δt2\Delta t_2.
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