Question

A block has a mass of 7 kg and on a surface with mhu= .7. Explain with forces, and prove mathematically, how the three situations could occur. A. The block is speeding up B. The block is slowing down C. The block is moving at a constant speed

Answer 1

A. F > 48.02 N

B. F < 48.02 N

C. F = 48.02 N

Explanation:

Given:

Mass (m) = 7 kg

µ = 0.7

Balancing horizontal forces:

`\begin{gathered} F=\mu N+ma\rightarrow F=\mu\cdot m\cdot g+ma \\ \text{ We replacing} \\ F=0.7\cdot7\cdot9.8+7a \\ F=48.02+7a \\ a=(F-48.02)/(7) \end{gathered}`

A. The block is speeding up

It means the block is having a positive value of acceleration:

`\begin{gathered} a>0 \\ (F-48.02)/(7)>0 \\ F>48.02\text{ N} \end{gathered}`

B. The block is slowing down

`\begin{gathered} a<0 \\ (F-48.02)/(7)<0 \\ F<48.02\text{ N} \end{gathered}`

C. The block is moving at a constant speed

`\begin{gathered} a=0 \\ (F-48.02)/(7)=0 \\ F=48.02\text{ N} \end{gathered}`