Respuesta :
Answer:
(a) 19.62 N
(b) Box moves down the slope
(c) 24.43 N
Explanation:
(a)
2 Kg box causes tension
[tex]T=mg
where m is mass, g is gravitational force taken as 9.81
T=2*9.81 =19.62 N
(b)
Block mass of 4 Kg
[tex]T'-mg sin \theta=0[/tex] hence [tex]T'=mg sin \theta[/tex] where m is mass and g is gravitational force
T'=4*9.81 sin 35= 22.5071 N
Since T' is greater than [tex]mg sin\theta[/tex] , then the box moves down the slope
(c)
Acceleration a= [tex]\frac {forward force-backward force}{Total mass}= \frac {mg sin \theta -mg}{m1 + m2}[/tex]
[tex]a= \frac {22.51-19.62}{2+4}=0.48 [/tex]
When moving, the box will exert force T"= [tex]mgsin \theta + ma[/tex]
T"= 4*9.81 sin 35 +(4*0.48)= 24.43 N
Answer:
(a). The tension in the string if the 4 kg box held in place is 22.48 N.
(b). The 4 kg box moves on downward.
(c). The tension in the string once the box begins to move is 24.4 N.
Explanation:
Given that,
Mass of box m₁ =4 kg
Mass of second box m₂= 2 kg
Angle = 35°
(a). We need to calculate the tension in the string if the 4 kg box is held in place, so that it cannot move
Using formula of tension
[tex]T=mg\sin\theta[/tex]
Put the value into the formula
[tex]T=4\times9.8\times\sin35[/tex]
[tex]T=22.48\ N[/tex]
(b). If the box is then released, which way will it move on the slope
We need to calculate the tension for block of mass 2 kg
[tex]T'=mg[/tex]
put the value into the formula
[tex]T'=2\times9.8[/tex]
[tex]T'=19.6\ N[/tex]
Here, T > T'
So, the first block moves on downward.
(c). We need to calculate the acceleration
Using formula of acceleration
[tex]a =\dfrac{forward\ force-bacward\ force}{total\ mass}[/tex]
[tex]a=\dfrac{T-T'}{M}[/tex]
Put the value into the formula
[tex]a=\dfrac{22.48-19.6}{6}[/tex]
[tex]a=0.48\ m/s^2[/tex]
We need to calculate the tension in the string once the box begins to move
For mass 4 kg
Using balance equation
[tex]T-T''=ma[/tex]
[tex]T''=T+ma[/tex]
Put the value into the formula
[tex]T''=22.48+4\times0.47[/tex]
[tex]T''=24.4\ N[/tex]
Hence, (a). The tension in the string if the 4 kg box held in place is 22.48 N.
(b). The 4 kg box moves on downward.
(c). The tension in the string once the box begins to move is 24.4 N.
