Question

A $2.0$-m-long, $500g$rope pulls a $10kg$ block of ice across a horizontal, frictionless surface. The block accelerates at $2.0m/s^2$ . How much force pulls forward on (a) the ice, (b) the rope? Assume that the rope is perfectly horizontal.

Short answer

(a)The pulling force on the ice is$20N$

(b) The pulling force on the rope is$21N$

Step-by-step solution

Given information (part a)

Length of rope$L=2m$

Mass of the rope, $m=0.5kg$

Mass of the block,$M=10kg$

Explanation (part a)

The pulling force on the ice is

$$\begin{gathered} F=ma \\ m=10kg \end{gathered}$$

Acceleration of the block localid="1649673133341" $a=2m/s^2$

localid="1649613259536" $$\begin{gathered} F=\left(10kg\right)\left(2m/s^2\right) \\ =20N \end{gathered}$$

The pulling force on the ice is $20N$

Given information (part b)

Length, $L=2m$

Mass of the rope, $m=0.5kg$

Mass of the block,$M=10kg$

Explanation (part b)

Force on the rope,$F_r$

localid="1649613290873" $$\begin{gathered} F_r=Ma+ma \\ M=10kg \\ m=0.5kg \\ a=2m/s^2 \\ {F}_r=\left(10kg\right)\left(2m/s^2\right)+\left(0.5kg\right)\left(2m/s^2\right) \\ =21N \end{gathered}$$

The pulling force on the rope is$21N$