Work problem and newtons laws?

Question

Doug pushes a 5.30 kg crate up a 2.10-m-high 20 degree frictionless slope by pushing it with a constant horizontal force of 22.0 N. What is the speed of the crate as it reaches the top of the slope? Solve this problem using work and energy, and then using Newton's laws.

Answer 1

Mass:
m = 5.3 kg

Slope:
α = 20º

Force:
F = F₁*cos(α) – m*g*sin(α) = (22 N)*(cos 20º) – (5.3 kg)*(9.81 m/s²)*(sin 20º) = 2.89 N

Acceleration:
a = F/m = (2.89 N)/(5.3 kg) = 0.53 m/s²

Displacement:
s = (2.1 m)/(sin 20º) = 6.14 m

Speed:
v = √(2*a*s) = √[2*(0.53 m/s²)*(6.14 m) = 2.55 m/s

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