Question

1. inertia is dependent on

a. the mass of the object
b. the velocity of the object
c. both the mass and velocity of the object
d. neither the mass nor velocity of the object

1. ______ equilibrium is a state of balance on non - moving objects. ______ equilibrium is a state of balance on moving objects. fill in the blanks.
2. which of the following is not true about an object in equilibrium?

a. it has no net force.
b. it has constant velocity.
c. it has constant acceleration.
d. the forces acting on it are balanced

1. what is the net force of a 72 - kg object moving with an acceleration of 3.6m/s² to the left?
2. in newton’s second law of motion, acceleration and mass are ______ proportional, and acceleration and force are ______ proportional.
3. a 25 - kg box is sliding across the floor

a. if the net force is 60 n left, what is the acceleration of the box?
b. if the net force is 60 n left, find the missing force x.
c. what is the value of the unlabeled downward force?
d. what is the value of the unlabeled upward force?

Explanation:

Step1: Recall inertia concept

Inertia is the tendency of an object to resist changes in its state of motion and depends on the mass of the object only.

Step2: Recall equilibrium definitions

Static equilibrium is for non - moving objects and dynamic equilibrium is for moving objects with constant velocity.

Step3: Analyze object in equilibrium

An object in equilibrium has no net force, constant velocity and balanced forces. Constant acceleration means there is a net force, so it's not true for an object in equilibrium.

Step4: Use Newton's second law for net - force calculation

Newton's second law is $F = ma$. Given $m = 72$ kg and $a=3.6$ m/s², then $F=72\times3.6 = 259.2$ N.

Step5: Recall Newton's second law proportionality

In $F = ma$, acceleration and mass are inversely proportional, and acceleration and force are directly proportional.

Step6: Calculate acceleration of the box

Using $F = ma$, with $F = 60$ N and $m = 25$ kg, then $a=\frac{F}{m}=\frac{60}{25}=2.4$ m/s².

Step7: Find the missing force x

Let the known left - hand force be $F_1$ and the right - hand force be $F_2$. If the net force $F_{net}=60$ N to the left and $F_1$ is known and $F_2=x$, then $F_{net}=F_1 - x$. We need to know $F_1$ to solve for $x$ exactly. Assuming the known left - hand force is $F_1 = 25$ N, then $x=F_1 - F_{net}=25 - 60=- 35$ N (the negative sign means it acts to the right).

Step8: Determine downward and upward forces

In the vertical direction, if the box is on a flat surface and there is no vertical acceleration, the downward force is the weight $W = mg$ where $m = 25$ kg and $g = 9.8$ m/s², so $W=25\times9.8 = 245$ N. The upward force (normal force) is equal in magnitude to the weight for no vertical acceleration, so it is also 245 N.

Answer:

1. a. The mass of the object
2. Static; Dynamic
3. c. It has constant acceleration
4. 259.2 N
5. Inversely; Directly

19.
a. 2.4 m/s²
b. Assuming left - hand force of 25 N, $x = - 35$ N (acts to the right)
c. 245 N
d. 245 N