Astudent moves a box of books down the hall by pulling on a rope attached to the box. the student pulls with a force of 171 n at an angle of 30.7 ◦ above the horizontal. the box has a mass of 38.9 kg, and µk between the box and the floor is 0.19. find the acceleration of the box.

-2.34 ms⁻²

Step-by-step explanation:

As per the question,

We have been provided the information that is

 Force at an angle 30.7° = 171 N

Mass of the box = 38.9 kg

Coefficient of friction between box and the floor = 0.19

Now,

By drawing the free body diagram and taking the horizontal and vertical component for force 171 N(as show below)

`At equilibrium:

N + 171 sin 30.7° = mg          ...................equation (i)

ma + 171 cos 30.7° = f           ..................equation (ii)

Where,

f = frictional force

As we know that,

Frictional force is given by:

f = μN

Where,

μ = coefficient of friction

N = normal reaction

From equation (i)

N = mg - 171 sin 30.7°

∴ f = μ ( mg - 171 sin 30.7°)     ............equation (iii)

From equation (ii) and (iii), we get

ma + 171 cos 30.7° = μ ( mg - 171 sin 30.7°)

Put the value of mass, μ and g  = 9.8 m/s²

(38.9)a + 171 cos 30.7° = 0.19 × ( (38.9 × 9.8) - 171 sin 30.7°)

(38.9)a + 146.889 = 55.861

a = -2.34 ms⁻²

Hence, the acceleration of the box is = - 2.34 ms⁻²

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )

the answer is:

the lateral area is equal to

to find the lateral area of the square pyramid, first we need to find the perimeter of the base, and then, find the lateral area using the following formulas:

where,

s, is the base length

slant height, is the height of a the side of the pyramid

we are given:

now, calculating the perimeter of the base, we have:

then, calculating the lateral area:

hence, we have that the lateral area is equal to

have a nice day!