A man of mass 80 kg is riding on a small cart of mass 40 kg which is rolling along a level flo

step 1 In this question we have given a man of mass 80 kilograms and it is riding on a small cart whose

A man of mass 80 kg is riding on a small cart of mass 40...

A man of mass $80 \mathrm{~kg}$ is riding on a small cart of mass $40 \mathrm{~kg}$ which is rolling along a level floor at a speed of 2 $\mathrm{m} / \mathrm{s}$. He is running on the cart so that his velocity relative to the cart is $3 \mathrm{~m} / \mathrm{s}$ in the direction opposite to the motion of the cart. What is the speed of the centre of mass of the system? (a) $1.5 \mathrm{~m} / \mathrm{s}$ (b) $1 \mathrm{~m} / \mathrm{s}$ (c) $3 \mathrm{~m} / \mathrm{s}$ (d) Zero

A man of mass $80 \mathrm{~kg}$ is riding on a small cart of mass $40 \mathrm{~kg}$ which is rolling along a level floor at a speed of 2 $\mathrm{m} / \mathrm{s}$. He is running on the cart so that his velocity relative to the cart is $3 \mathrm{~m} / \mathrm{s}$ in the direction opposite to the motion of the cart. What is the speed of the centre of mass of the system?
(a) $1.5 \mathrm{~m} / \mathrm{s}$
(b) $1 \mathrm{~m} / \mathrm{s}$
(c) $3 \mathrm{~m} / \mathrm{s}$
(d) Zero

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Center of Mass

This concept refers to the weighted average position of the components of a system, where the weights are the masses of the objects. The velocity of the center of mass is determined by the total momentum of the system divided by its total mass. For an isolated system (or one where external net forces are negligible), the center?of-mass velocity remains constant even when internal forces (like a person running on a cart) cause changes in the individual velocities of the parts.

Conservation of Momentum

In the absence of net external forces, the total momentum of a system is conserved. This means that any internal actions, such as one part of the system accelerating relative to another, will not alter the overall momentum of the system. Instead, the momentum redistributed among the constituents still sums to the original total, ensuring that the center?of-mass motion remains unaffected.

Relative Motion

This involves analyzing the motion of one object with respect to another. Here, understanding the velocity of the man relative to the cart and how that translates into their velocities relative to the ground is key. Once the relative motion is properly accounted for, it can be combined with momentum conservation to determine the final absolute velocities and, consequently, the center-of-mass speed of the system.

Transcript

Please give Ace some feedback