The wind pushes a cup along the sand at the beach. the force of the wind was 17.8n, and the opposing force was 2n. if the cup accelerates at 7m/s^2, how much does the cup weigh?

Explanation:

Let's begin with the cup's free body diagram (figure attached), there we are able to see the forces acting on this object:

On the X axis:

  (1)

Where:

is the force of the wind

is the opposing force (that is why it has the negative sign)

So:

  (2)

In addition we know by Newton's 2nd law:

  (3)

Where:

is the mass of the cup

is its acceleration

Substituting (2) in (3):

  (4)

Finding :

  (5)

On the other hand we have the forces acting on the Y axis:

  (6)

Where:

is the normal force

is the weight of the cup, being the acceleration due gravity

This means:

  (7)

Substituting (5) in (7):

  (8)

Finally:

  This is the weight of the cup

seeing the graph would