Answer:
49 N
Explanation:
According to Newton's second law of motion, the net force on an object is equal to its mass times its acceleration. By drawing a free body diagram, we can determine the forces on each mass and then apply Newton's law.
For the block, there are three forces:
Weight force mg pulling down,
Normal force N₁ pushing right,
Friction force N₁μ pushing up.
For the cart, there are five forces:
Weight force Mg pulling down,
Normal force N₂ pushing up,
Applied force F pushing to the right,
Normal force N₁ pushing left,
Friction force N₁μ pushing down.
Sum of forces on the block in the y direction:
∑F = ma
N₁μ − mg = 0
N₁μ = mg
Sum of forces on the block in the x direction:
∑F = ma
N₁ = ma
Substitute:
maμ = mg
aμ = g
a = g/μ
a = (9.8 m/s²) / (0.46)
a = 21.3 m/s²
Next, sum of forces on the cart in the x direction:
∑F = ma
F − N₁ = Ma
F − ma = Ma
F = (m + M) a
F = (0.2 kg + 2.1 kg) (21.3 m/s²)
F = 49 N
