A B C D E F G H I N 2. Velocity of the cart A B C D E F G H I N 3. Momentum of t
ID: 1556526 • Letter: A
Question
A B C D E F G H I N
2. Velocity of the cart
A B C D E F G H I N
3. Momentum of the cart
A B C D E F G H I N
4. Kinetic energy of the cart
A B C D E F G H I N
5. Potential energy of the spring
A B C D E F G H I N
6. Total mechanical energy of the cart (including the spring)
A B C D E F G H I N
A cart with a spring on the end of it is moving to the right (in the positive x direction) on a frictionless air track as shown in the figure at the right. The initial position of the cart is arbitrary. It keeps going until it hits a wall, the spring compresses, and the cart bounces off the wall and moves in the opposite direction. Select all the graphs that could represent each of the following quantities as a function of time. (In each graph, the axes cross at the origin of the two coordinates.) Put N if none of the answers work. 0Explanation / Answer
1) Position of the cart
Lets take the initial position of the cart at the arbitary position as x=-a and as the cart moves towards the wall, the position 'x' (distance between the cart and its starting point) will keep on increasing and will reach the maximum point when the cart touches the wall and bounces back due to the spring. Now the position 'x' will keep on decreasing as the cart returns towards the starting point.
Answer: Graph H perfectly describes the events.
2) Velocity of cart
The cart moves towards the wall with a constant velocity (since acceleration is not specified), so graph of velocity will be a straight line above x-axis until it reaches the wall and the cart bounces back. Since the cart moves in opposite direction, the velocity will now become negative but will remain constant with the same magnitude as before collision (since the spring is ideal and collision is perfectly elastic). Hence after rebounding, the velocity will be a straight line below x-axis.
Answer: Graph C perfectly describes the events
3) Momentum of cart
Since the mass remains constant, the momentum (P=m*v) will be only dependent on velocity and hence, will follow the same graph as velocity. The final momentum after collision will be equal to the initial momentum before collision as per law of conservation of momentum,
Answer: Graph C perfectly describes the events
4) Kinetic energy
KE = 1/2 m v2 , Since mass and velocity remains constant throughout the event, the KE will be constant and positive before and after the coliision. But during the collision as the spring presses against the wall and compresses, Some of the KE in the cart starts transforming into PE in the spring and gets fully transformed into PE (KE =0) when compression reaches it max and cart is no longer moving in positive direction, So during this time, KE will decrease gradually and PE will increase correspondingly.
Answer: Graph E perfectly describes the events
5) Potential energy
PE developes only when the spring is compressed against the wall and reaches max when the spring and fully compressed, and decreases back to 0 when the spring is free from any compression and the cart rebounds.
Answer: Graph G perfectly describes the events
6) Mechanical energy
ME = PE + KE is also known as total energy is the sum of PE and KE and is always conserved and constant (givenby the law of conservation of energy) Hence ME will be a straight line above the x-axis for the entire time.
Answer: Graph A perfectly describes the events
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