The following is the question:
"When a 2-kg object is moving on a slope with an inclination of 30 degrees,what is its acceleration?"
I have been trying to solve the question for 10 times,but I still get the wrong answer(15m/s^-2),but not the correct one(approximately 3.27m/s^-2).Could you help with my question?
I am not sure about whether or not there is friction. If friction exists, then it reduces the net force, and therefore the acceleration, acting on the object. I would prefer to have it clearly said in a problem whether or not to consider friction. But usually if friction is not mentioned, then the student should assume zero friction -- which simplifies the question. If it is correct to assume no friction in this problem, then I can't see how the correct answer would be as low an amount as you indicate. Let me go through the work to show you what the answer should be if we ignore friction.
The weight is W = m*g = 2 kg*9.8 m/s^2 = 19.6 N (N for Newtons).
That weight is a force pointing vertically down. The object will accelerate down the slope due to a component of that force, Fds, pointing down the 30 degree slope. Finding the value of Fds requires trigonometry to find the fraction of the weight that acts down the slope.
Fds = 19.6 N*sin30 = 9.8 N
The rate of acceleration is given by Newton's 2nd Law.
Fnet = m*a
The net force in this case is Fds.
Fds = m*a
9.8 N = 2 kg*a
a = 9.8 N / 2 kg = 4.9 m/s^2
That is the acceleration of any object sliding down a frictionless 30 degree incline (on Earth where the free-falling acceleration due to gravity is 9.8 m/s^2).
Note: You used incorrect units when you gave the accelerations that you obtained and that you believe to be the correct answer. The units for acceleration could be either of these 2 options:
m.s^-2 or m/s^2
I hope this helps,