# A 50-kg block of cement is pulled upward (not sideways) with a force of 800N. What is the acceleration of the block?The answer is 6.0 m/s^2 , but how do I get the answer?

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### 2 Answers

The 50 kg block of cement is being pulled upwards with a force of 800 N. When a force F is applied on an object with mass m it is accelerated by a, where the three quantities are related by F = m*a.

As the mass of the block is 50 kg and the force with which it is lifted upwards is 800 N, we have 800 = 50*a or a = 800/50 = 16 m/s^2.

It is assumed that the block is on Earth. The gravitational force of attraction on Earth accelerates all objects downwards by an acceleration with magnitude 9.8 m/s^2.

As the block is being accelerated downwards by 9.8 m/s^2 due to the gravitational force and upwards by 16 m/s^2 due to the force lifting it, the net acceleration of the block is 16 - 9.8 = 6.2 m/s^2 upwards.

All forces acting on a body should be considered to be able to estimate the correct acceleration of the body.

When you get a problem like this, always start off with what the question is asking for. In this case, we're looking at acceleration. We see a lot of forces involved, so it's safe to say we're going to need Newton's second law:

`F(net)=ma`

Mass is given to you, but force is the "net force." We'll need to combine all of the forces on the block to find the net force.

Start off by diagramming the forces on the block. In the vertical axis, we have to worry about two forces: gravity downward (F(gravity)=mg) and the applied force (800N upwards). Because we're not moving the cement block sideways, we don't have to worry about friction or any other left-right forces.

In case you're worried about axes, let's just say that "up" is positive. Because of this, we can now say which force is negative and which is positive. Because our applied force is going "up," it will be a positive 800N. Because gravity is going "down," it will be -mg.

Our net force can now be found as follows by combining the two forces we know are acting on the block:

`F(net) = F(gravity)+F(applied)`

`F(net) = -mg + 800N`

Setting `m = 50 kg` and `g = 10 m/(s^2)`:

`F(net) = -(50)(10) + 800 = -500 + 800 = 300N`

We now know the net force acting on the block is 300 N upwards. Now we can use Newton's Second Law to solve for the acceleration:

`F(net) = ma`

`300 = 50a`

`a = 6 m/(s^2)`

And there you have it!