A box with a mass of 34 kg slides along a frictionless board resting at an angle of 34 degrees to the horizontal. What is the acceleration of the box?
The box slides down a frictionless board. Since, the board is at an angle, we can resolve the weight component of the box in two different components: horizontal to the board and vertical to the board. The weight of the box is in vertically downward direction (due to gravity) and its component along the board (pointing downwards) is given as mg sin 34, where m is the mass of the box (given as 34 kg), g is acceleration due to gravity and the angle of the incline is given as 34 degrees. Similarly the vertical component of the force (in relation to the board) is given as mg cos 34.
Using, Newton's second law, force is the product of mass and acceleration; and since the box is free to slide down, we can deduce,
F = ma = mg sin 34
or, acceleration, a = g sin 34 = 5.91 m/s^2.
Hope this helps.