Question

Three people are pushing a 200kg sofa to the right with forces of 50N to the right, 75N to the right, and 20N to the left (not sure what is motive is). What is the acceleration of the sofa?

A) 0.53 m/s² to the right
B) 0.725 m/s² to the right

Answer 1

The acceleration of the sofa is found by summing the forces and then applying Newton's second law of motion. The net force is 105N to the right, and with a mass of 200kg, the acceleration is calculated to be 0.525 m/s² to the right, which rounds to option A) 0.53 m/s².

Step-by-step explanation:

The question involves calculating the acceleration of a sofa being pushed by three people. To find the net force acting on the sofa, we sum the forces applied to the right and subtract the force applied to the left: 50N (right) + 75N (right) - 20N (left) = 105N (net force to the right).

Next, we use Newton's second law of motion, F = ma, where F is the net force acting on the object, m is the mass, and a is the acceleration. The mass of the sofa is given as 200kg. We can rearrange the formula to solve for acceleration, a = F / m.

Substituting the net force and mass into the equation gives us a = 105N / 200kg, which results in an acceleration of 0.525 m/s² to the right. The closest answer choice to this calculated value is A) 0.53 m/s² to the right.