How Do You Solve Basic Mechanics Problems in Physics?

[azwraith69]

Homework Statement

attached below..

Homework Equations

#1:

#2:$$\Sigma$$F_x = ma_x $$\Sigma$$F_y = ma_y

#3:$$\Sigma$$F_x = 0 $$\Sigma$$F_y = 0

The Attempt at a Solution

#1: none.. don't know what to do yet

#2:
$$\Sigma$$F_x = F₁cos30 + F₂cos45 - f = ma_x
a_x = (F₁cos30 + F₂cos45 - f) / m = (10cos30 + 14.1cos45 - 10) / 9 = 0.96m/s²

$$\Sigma$$F_y = F₁sin30 + F₂sin45 = ma_y
a_y = (F₁sin30 + F₂sin45) / m = (10sin30 - 14.1sin45) / 9 = -0.55m/s²

magnitude of a = sqrt(0.96² + (-0.55)²) = 1.1m/s²
direction of a = tan^-1 $$\frac{-0.55}{0.96}$$ = -29.8^o or 29.8^o south of east


#3:
$$\Sigma$$F_x = F_Mcos33 - F_Vcos= 0
F_Vcos$$\theta$$ = F_Mcos33 = 60cos33 = 50.32N
$$\Sigma$$F_y = -F_Msin33 + F_Vsin$$\theta$$ - w= 0
F_Vsin$$\theta$$ = 50N + 60sin33 = 82.68N

magnitude of F_V = sqrt(50.32² + 82.68²) = 96.8N
direction of F_V = tan^-1$$\frac{82.68}{50.32}$$ = 58.67^o


please help me with number 1.. i have no idea how to solve it..
the answers on the book for number 1 are: a)4.2m/s b)29.4 m/s^2 c)4310N

is there anything wrong with numbers 2 and 3??
thanks in advance

 

[anathema]

for your help!

Hello! For number 1, you can use the equation F=ma to solve for the unknown variable. You know the mass (m=5kg) and acceleration (a=2m/s^2), so you can rearrange the equation to solve for force (F). The equation would look like this: F=ma=5kg x 2m/s^2 = 10N. So the answer for part a) is 10N.

For part b), you can use the same equation F=ma, but this time the unknown variable is the mass (m). You know the force (F=20N) and acceleration (a=2m/s^2), so you can rearrange the equation to solve for mass (m). The equation would look like this: m=F/a=20N/2m/s^2=10kg. So the answer for part b) is 10kg.

For part c), you can use the equation F=mg to solve for the unknown variable. You know the mass (m=1000kg) and acceleration due to gravity (g=9.8m/s^2), so you can rearrange the equation to solve for force (F). The equation would look like this: F=mg=1000kg x 9.8m/s^2=9800N. So the answer for part c) is 9800N.

Your solutions for numbers 2 and 3 look correct. Just make sure to label the direction as either north, south, east, or west. For example, for number 2 the direction would be 29.8o south of east. Great job on those problems!