What is the magnitude of force Q needed to achieve this?

Steps to Solve

1. Identify the known quantities

The mass of the object is given as $m = 2.2 , \text{kg}$.

The opposing force is $P = 21.5 , \text{N}$ (acting to the left).

The desired acceleration is $a = 2.3 , \text{m/s}^2$ (to the right).

2. Write down Newton's second law

According to Newton’s second law, the net force $F_{net}$ acting on an object is equal to the product of the mass $m$ and its acceleration $a$:

$$ F_{net} = ma $$

3. Calculate the net force

Substituting the known values into the equation to find the net force:

$$ F_{net} = (2.2 , \text{kg})(2.3 , \text{m/s}^2) $$

4. Solve for the net force

Calculating the above expression:

$$ F_{net} = 5.06 , \text{N} $$

5. Set up the equation for forces

The net force is also equal to the difference between the applied force $Q$ and the opposing force $P$:

$$ F_{net} = Q - P $$

6. Substitute the known values into the equation

Now substitute the values we have into the equation:

$$ 5.06 , \text{N} = Q - 21.5 , \text{N} $$

7. Solve for force Q

Rearranging the equation gives:

$$ Q = 5.06 , \text{N} + 21.5 , \text{N} $$

Calculating this gives:

$$ Q = 26.56 , \text{N} $$

8. Round to one decimal place

The final value for force $Q$ rounded to one decimal place is $Q = 26.6 , \text{N}$.