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Answer :
Final answer:
The acceleration of the wedge along the plane is 1.14 m/s^2.
Explanation:
To find the acceleration of the wedge along the plane, we need to consider the forces acting on the wedge. The force pushing the wedge horizontally is the driving force, F. The weight of the wedge is the force acting vertically downwards, given by mg, where m is the mass of the wedge and g is the acceleration due to gravity.
The component of the weight that acts parallel to the plane is mg*sin(theta). There is also a friction force, f, acting in the opposite direction of motion. The equation of motion for the wedge can be written as:
ma = F - mg*sin(theta) - f
We can solve this equation for a, the acceleration:
a = (F - mg*sin(theta) - f) / m
Substituting the given values:
a = (323.3 N - 37.9 kg * 9.81 m/s^2 * sin(22.1) - 0.101 * 37.9 kg * 9.81 m/s^2 * cos(22.1)) / 37.9 kg
a = 1.14 m/s^2
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