Question

A block sits on a frictionless sheet of ice. When it is pushed by a force of 15 N, the block will accelerate at a rate of 6.4 m/s^2. The block is then moved to the moon, where the acceleration of gravity is 1.62m/s^2. The coefficient of kinetic friction between the block and the moon's surface is 0.35. If the block is now pushed with the same force, what will be its acceleration?

Answer 1

`a_(moon)=5.84m/s^(2)`

Step-by-step explanation:

In order to solve this problem, we will need to draw a free body diagram of both situations (see attached picture).

So first, we need to find what the mass of the object is. We can do so by analyzing the horizontal movement of the first situation, so we get:

`\sum F_(x)=ma`

F=ma

`m=(F)/(a)`

so

`m=(15N)/(6.4m\s^(2))`

m=2.34kg

next, we can analyze the second situation, we will start by analizing the vertical movement so we can determine the Normal force, so we get:

`\sum F_(y)=0`

`N-W=0`

N=W

N=mg

`N=2.34kg(1.62 m/s^(2)`

N=3.79N

so now we can analyze the horizontal movement of the block, so we get:

`\sum F_(x)=ma`

`F-N\mu _(k)=ma`

`a=(F-N\mu_(k))/(m)`

`a=(15N-(3.79N)(0.35))/(2.34kg)`

`a=5.84 m/s^(2)`