Question

thinking and inquiry

1. a stationary box of mass 4.2 kg is given a push of 8.2 n s along a surface where the frictional force acting is 5.8 n n. the push lasts for 3.6 s and then the box is allowed to slide on its own until it comes to rest. (10 marks)

(a) draw free - body diagrams to show the box being pushed and sliding on its own.
(b) determine the acceleration of the box as it is being pushed.
(c) calculate the speed of the box just as the push ceases.
(d) determine the acceleration of the box as it is sliding on its own.

Explanation:

Step1: Identify Forces for Acceleration (Pushed)

Forces on the box when pushed: applied force \( F_{app} = 8.2\,\text{N [S]} \), friction \( F_f = 5.8\,\text{N [N]} \), mass \( m = 4.2\,\text{kg} \). Net force \( F_{net} = F_{app} - F_f \) (since opposite directions).
\( F_{net} = 8.2 - 5.8 = 2.4\,\text{N [S]} \).

Step2: Apply Newton's Second Law (\( F = ma \))

Solve for acceleration \( a \): \( a = \frac{F_{net}}{m} \).
Substitute values: \( a = \frac{2.4}{4.2} \approx 0.571\,\text{m/s}^2 \) [S].

Answer:

The acceleration of the box as it is being pushed is approximately \( \boldsymbol{0.57\,\text{m/s}^2} \) [South] (or \( 0.571\,\text{m/s}^2 \) [S]).