Question

problem 6: a chest 39 kg lies on the floor. a person tries to lift the chest by exerting a force of f1 = 200 n up. how much force does the floor exert on the chest? make sure to make a free body diagram showing all the forces acting on the crate before using newtons laws.

Explanation:

Step1: Calculate the weight of the chest

The weight $W$ of an object is given by $W = mg$, where $m = 39\ kg$ and $g=9.8\ m/s^{2}$. So $W=39\times9.8 = 382.2\ N$.

Step2: Apply Newton's first - law in the vertical direction

In the vertical direction, the sum of forces $\sum F_y = 0$ (since the chest is at rest). Let the normal force exerted by the floor be $N$. The upward forces are $F_1$ and $N$, and the downward force is $W$. So $\sum F_y=F_1 + N - W=0$.

Step3: Solve for the normal force $N$

We can re - arrange the equation $F_1 + N - W = 0$ to get $N=W - F_1$. Substitute $W = 382.2\ N$ and $F_1 = 200\ N$ into the equation. Then $N=382.2-200=182.2\ N$.

Answer:

$182.2\ N$