# Summing forces: finding acceleration and F_n

• cag805
In summary: So you should have F_g = -m * g = -539N.In summary, use the given steps to find the magnitude of the acceleration and normal force acting on a chair. Yusef pushes a chair of mass 55.0 kg across a carpeted floor with a force of 160 N directed at 35.0 degrees below the horizontal. The magnitude of the kinetic frictional force is 107N. The acceleration of the chair is 0.85 m/s^2 and the normal force is 631N.
cag805

1. Homework Statement

Use the steps outlined above to find the magnitude of the acceleration a of a chair and the magnitude of the normal force FN acting on the chair: Yusef pushes a chair of mass m = 55.0 kg across a carpeted floor with a force F⃗ p (the subscript 'p' here is lowercase and throughout the question) of magnitude Fp = 160 N directed at θ = 35.0 degrees below the horizontal (Figure 1) . The magnitude of the kinetic frictional force between the carpet and the chair is Fk = 107N .

What is the magnitude of the acceleration a of the chair? What is the magnitude of the normal force FN acting on the chair?
Express your answers, separated by a comma, in meters per second squared and Newtons to three significant figures.

## Homework Equations

ΣFx = Fpcosθ−Fk = m * a_x
ΣFy = FN−FG−Fpsinθ =m * a_y

## The Attempt at a Solution

a_x

a

F_n

Redo your calculation of the normal force. The applied force acts downward and thus must increase the normal force.

cag805
Ah that makes sense. However, in F_N = F_g + F_py, F_py = 160N * sin(325) which gives me a negative number. The problem states that the force is applied at -35 degrees. Intuitively,I now know that greater pushing force increases normal force... but what can I do when I'm given an angle like this? Maybe add 180 degrees?

cag805 said:
Ah that makes sense. However, in F_N = F_g + F_py, F_py = 160N * sin(325) which gives me a negative number. The problem states that the force is applied at -35 degrees. Intuitively,I now know that greater pushing force increases normal force... but what can I do when I'm given an angle like this? Maybe add 180 degrees?
Don't just plug in numbers blindly. What does the minus sign mean? Just that it points downward. So be consistent. If F_py is negative, so should F_g be negative. They both point down.

But leaving it as negative gives me the incorrect answer?

F_N = F_g + F_py = 539N + 160 * sin(325)
F_N = 539N - 91.77N = ~447N (incorrect)

F_N = F_g + F_py = 539N + 160 * sin(325 + 180)
F_N = 539N + 91.77N = ~631N(correct)

cag805 said:
But leaving it as negative gives me the incorrect answer?
You must be consistent. If that force is negative, so must be F_g. And the equation you want is ΣF_y = 0.

## 1. What is the formula for finding acceleration?

The formula for finding acceleration is: a = F_net / m, where a is acceleration, F_net is the net force acting on an object, and m is the mass of the object.

## 2. How do you calculate the net force?

The net force is calculated by adding all the individual forces acting on an object. If the forces are in the same direction, they can simply be added together. If the forces are in opposite directions, the larger force is subtracted from the smaller force to get the net force.

## 3. What is the difference between mass and weight?

Mass is a measure of the amount of matter an object contains, while weight is a measure of the force of gravity acting on an object. Mass is measured in kilograms, while weight is measured in newtons.

## 4. How does the normal force affect an object's motion?

The normal force is the force exerted by a surface on an object in contact with it. It acts perpendicular to the surface and counteracts the force of gravity. The normal force is an important factor in determining an object's motion, as it helps to balance out other forces and keep the object in equilibrium.

## 5. Can an object have a net force of zero and still be accelerating?

Yes, an object can have a net force of zero and still be accelerating if there are other unbalanced forces acting on it. For example, if an object is moving in a circular motion, the net force may be zero but the object is still accelerating towards the center of the circle due to the centripetal force.

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