Question

Bob is pushing a box across the floor at a constant speed of , applying a horizontal force whose magnitude is$\mathbf{20}\mathbf{}\mathit{N}$ . Alice is pushing an identical box across the floor at a constant speed of $\mathbf{2}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}$, applying a horizontal force. (a) What is the magnitude of the force that Alice is applying to the box? (b) With the two boxes starting from rest, explain qualitatively what Alice and Bob did to get their boxes moving at different constant speeds.

Short answer

a) The force that Alice is exerting on the box is .

b) Alice and Bob initially applied force is large than the static friction, so the box starts moving; when the desired speed is reached, the force is reduced, resulting in a net force of zero.

Step-by-step solution

Identification of given data

• Bob is pushing the box with constant speed,$v_b=1m/s$
• Alice is pushing the box with constant speed,$v_a=2m/s$
• Bob applying horizontal force,$F_b=20N$

Significance of Newton’s 2nd law of motion

Newton’s 2^nd law of motion is, the formula F = ma is crucial because it depicts the connection between forces and motion. It enables you to compute an object's acceleration (and hence velocity and direction) using known forces.

This is extremely useful for scientists, engineers, inventors, and other professionals. We can map out an object's trajectory by regulating, measuring, or estimating the force exerted on it and so know where it will be at any given moment.

Calculating the force is applied to the box

Part a)

By applying Newton's 2^nd Law of motion,

$\sum _{}F=ma$

Where is force is applied, is the mass of the box, is the acceleration of the box.

Here constant speed, which means acceleration is zero.

$$\begin{gathered} F_a-F_b=0 \\ {F}_a=F_b \\ {F}_a=20N \end{gathered}$$

Thus, the force that Alice is exerting on the box is .

Condition for constant speed

Part b)

Alice applied a larger force at first to accelerate the box that required some speed, then gradually decreased the external force to keep the speed constant.

Thus,Alice and Bob initially applied force is large than the static friction, so the box starts moving; when the desired speed is reached, the force is reduced, resulting in a net force of zero.