Respuesta :
Answer:
(a). The acceleration of the system is 1.65 m/s².
(b). The force that each crate exerts on the other is 426.75 N.
(c). The force that each crate exerts on the other when the crates reversed is 221.91 N.
Explanation:
Given that,
Mass of first crates = 65 kg
Mass of second crates = 125 kg
Force = 650 N
Coefficient of kinetic friction = 0.18
(a). We need to calculate the acceleration of the system
Using balance equation
[tex](m_{1}+m_{2})a=F-F_{fr}[/tex]
[tex](m_{1}+m_{2})a=F-\mu(m_{1}+m_{2})g[/tex]
[tex]a=\dfrac{F}{(m_{1}+m_{2})}-\mu g[/tex]
Put the value into the formula
[tex]a=\dfrac{650}{65+125}-0.18\times9.8[/tex]
[tex]a=1.65\ m/s^2[/tex]
(b). We need to calculate the force that each crate exerts on the other
Using balance equation
[tex]F-F_{fr}=m_{2}a[/tex]
[tex]F=m_{2}a+\mu m_{2}g[/tex]
Put the value into the formula
[tex]F=125\times1.65+0.18\times125\times9.8[/tex]
[tex]F=426.75\ N[/tex]
(c). If the crates reversed,
We need to calculate the force that each crate exerts on the other
Using balance equation
[tex]F-F_{fr}=m_{2}a[/tex]
[tex]F=m_{2}a+\mu m_{2}g[/tex]
Put the value into the formula
[tex]F=65\times1.65+0.18\times65\times9.8[/tex]
[tex]F=221.91\ N[/tex]
Hence, (a). The acceleration of the system is 1.65 m/s².
(b). The force that each crate exerts on the other is 426.75 N.
(c). The force that each crate exerts on the other when the crates reversed is 221.91 N.
Answer:
Explanation:
m = 65 kg
M = 125 kg
F = 650 N
μ = 0.18
(a) Let a be the acceleration of the system
Let f be the force of contact between the two.
use newton's second law
F - f - μmg = m x a .... (1)
f - μMg = M x a... (2)
Add both the equations
F - μ(M + m) g = (M + m) a
650 - 0.18 (65 + 125) x 9.8 = (65 + 125) a
a = 1.657 m/s²
(b) Put the value in equation (2)
f - 0.18 x 125 x 9.8 = 125 x 1.657
f = 207.125 + 220.5
f = 427.625 N
(c) if the crates are reversed, the acceleration remains same.
f - 0.18 x 65 x 9.8 = 65 x 1.657
f - 114.66 = 107.705
f = 222.365 N
