**Problem:**Bob pushes on a frictionless cart of mass 6.8 kg, and the cart has an acceleration of 5.7 m/s². If Bob now pushes twice as hard on a cart with twice the mass, what will be the acceleration of the heavier cart?**Solution:**To find the acceleration of the heavier cart when Bob pushes twice as hard, we follow these steps:Given:- Initial mass of the cart (m₁) = 6.8 kg- Acceleration of the cart (a₁) = 5.7 m/s²- Force exerted by Bob (F) = m₁ * a₁We need to determine:- The acceleration (a₂) of the new cart with twice the mass when Bob pushes with twice the force.Step-by-step calculation:1. Calculate the force Bob initially exerts: \[ F = m₁ \cdot a₁ = 6.8 \text{ kg} \cdot 5.7 \text{ m/s}^2 = 38.76 \text{ N} \]2. If Bob pushes twice as hard, the force will be: \[ F_{\text{new}} = 2 \cdot F = 2 \cdot 38.76 \text{ N} = 77.52 \text{ N} \]3. The new cart has twice the mass: \[ m₂ = 2 \cdot m₁ = 2 \cdot 6.8 \text{ kg} = 13.6 \text{ kg} \]4. Using Newton's second law, calculate the acceleration (a₂) of the heavier cart: \[ a₂ = \frac{F_{\text{new}}}{m₂} = \frac{77.52 \text{ N}}{13.6 \text{ kg}} \]5. Compute the result: \[ a₂ = 5.7 \text{ m/s}^2 \]Thus, the acceleration of the heavier cart will be \( 5.7 \text{ m/s}^2 \).

Given: The mass of the cart is 6.8 kg. The acceleration of the cart is 5.7 m/s2.

Bob pushes on a frictionless cart of mass 6.8 kg and the cart has an acceleration of 5.7 m/s2. If Bob now pushes twice as hard on a cart with twice the mass, what will be the acceleration of the heavier cart? Your Answer:

Bob pushes on a frictionless cart of mass 6.8 kg and the cart has an acceleration of 5.7 m/s2. If Bob now pushes twice as hard on a cart with twice the mass, what will be the acceleration of the heavier cart? Your Answer:

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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