Answer:
(B) 5.34 m/s
Step-by-step explanation:
We can solve this with forces or with energy.
First, let's solve using forces.
The sum of the forces on the sphere in the y direction is:
∑F = ma
T − Mg = M(-a)
T = Mg − Ma
The sum of the forces on the block parallel to the incline is:
∑F = ma
T − F − mg sin θ = ma
Substituting and solving for a:
Mg − Ma − F − mg sin θ = ma
Mg − F − mg sin θ = (m + M) a
a = (Mg − F − mg sin θ) / (m + M)
a = (4×9.8 − 2 − 3×9.8×⅗) / (3 + 4)
a ≈ 2.79 m/s²
So the velocity after 5 meters of travel is:
v² = v₀² + 2a(x - x₀)
v² = (0)² + 2(2.79)(5)
v ≈ 5.29 m/s
Using energy:
Potential energy = Potential energy + Kinetic energy + Work
MgH = mgh + ½ Mv² + ½ mv² + Fd
(4)(9.8)(5) = (3)(9.8)(3) + ½ (4)v² + ½ (3)v² + (2)(5)
196 = 88.2 + 3.5 v² + 10
v ≈ 5.29 m/s
The closest answer is B, 5.34 m/s.