Resolving Forces: Acceleration & Speed of 4kg Block on Inclined Plane

[hasnain721]

Homework Statement

A block of wood of mass 4 kg is released from rest on a plane inclined at 30 degrees to the horizontal. Assuming that the surface can be modeled as smooth (no friction) calculate the acceleration of the block, and its speed after it has moved 3m

Homework Equations

equations of motion

The Attempt at a Solution

http://img174.imageshack.us/img174/2632/36018360et2.jpg

 

[Rudipoo]

Apply F = ma down the slope by calculating the component of the weight down the slope to find the accleration. Then use v^2 = u^2 + 2as to find the velocity v after s = 3 metres. Hope this helps.

 

[Moetasim]

The acceleration of the block can be calculated using the equation F=ma, where F is the net force acting on the block and m is its mass. Since there is no friction acting on the block, the only force acting on it is its weight, which is given by the equation mg, where g is the acceleration due to gravity.

In this case, the weight of the block can be resolved into two components: one parallel to the incline and one perpendicular to the incline. The component parallel to the incline is given by mg sin 30 degrees, while the component perpendicular to the incline is given by mg cos 30 degrees.

Since the block is released from rest, its initial velocity is 0 m/s. Using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, we can solve for the final velocity of the block after it has moved 3m.

Plugging in the values, we get v^2 = (0)^2 + 2(9.8 m/s^2)(3m) = 58.8 m^2/s^2. Taking the square root, we get v = 7.67 m/s.

Therefore, the acceleration of the block is 9.8 m/s^2 and its final speed after moving 3m is 7.67 m/s. It is important to note that this solution assumes no air resistance or other external forces acting on the block. In real life, there may be slight variations due to these factors.