Answer:
(a) a= 0.74 m/s²
(b) a= 7.26 m/s²
Explanation:
Known data
a)m= 310 kg , : crate mass
F = 450 N which is inclined at an upward angle θ = 38° to the horizontal, in direction of the motion
f= 125 N opposes the motion.
b)W = 310 N :crate weight
F = 450 N which is inclined at an upward angle θ = 38° to the horizontal, in direction of the motion
f= 125 N opposes the motion
F component in x
Fx= F*Cosθ = 450*Cos38°
Fx= 354.6 N
F component in y
Fy= F*sinθ = 450*sin38°
Fy= 277.05N
Newton's second law:
∑F = m*a (Formula 1)
∑F : algebraic sum of the forces in Newton (N)
m : mass in kilograms (kg)
a : acceleration in meters over second square (m/s²)
Problem development
We choose the positive direction, the direction of the crate's movement and apply equation 1:
a)∑Fx = m*a
Fx-f= m*a
354.6 - 125 = 310*a
310*a = 229.6
[tex]a= \frac{229.6}{310}[/tex]
a= 0.74 m/s²
b) ∑Fx = m*a , m= W/g = 310/9.8 =31.63 N
Fx-f= m*a
354.6 - 125 = 31.63*a
31.63*a = 229.6
[tex]a= \frac{229.6}{31.63}[/tex]
a= 7.26 m/s²
