Question

A student solving for the acceleration of an object has applied appropriate physics principles and obtained the expression a = a1 + Fm where a1 = 3.00 m/s2, F = 12.0 kg.m/s2 and m = 7.00 kg. First, which of the following is the correct step for obtaining a common denominator for the two fractions in the expression in solving for a?

a. (m/m times a1/1) + (1/1 times F/m).
b. (1/m times a1/1) + (1/m times F/m).
c. (m/m times a1/1) + (F/F times F/m).
d. (m/m times a1/1) +(m/m times F/m ).

Answer 1

`A. \ a = ((m)/(m)* (a_1)/(1)) + ((1)/(1)* (F)/(m))`

Step-by-step explanation:

Given the expression for calculating the acceleration as shown;

`a = a_1 + (F)/(m)` where;

`a_1 = 3.00m/s^2\\\\F = 12.0kg.m/s^2\\\\m = 7.00kg\\`

To get the correct step for obtaining a common denominator for the two fractions in the expression in solving for a, we will find the LCM of the given expression as shown;

`a = a_1 + (F)/(m)\\\\a = (a_1)/(1)+(F)/(m)\\ \\a = ((m*a_1)+F)/(m) \\\\a = (ma_1+F)/(m)\\ \\a = ((m)/(m)* (a_1)/(1)) + ((1)/(1)* (F)/(m))`

The final expression gives the requires step. On substituting the given parameters into the resulting expression to get a;

`a = ((7)/(7)* (3)/(1)) + ((1)/(1)* (12)/(7))\\\\a = (21)/(7) + (12)/(7)\\ \\a = (21+12)/(7)\\ \\a = (33)/(7) m/s^2`