Find the magnitude of the block's acceleration

[TS656577]

Homework Statement

Refer to Fig. 5-38 (see below). Let the mass of the block be 2.3 kg and the angle x be 20°. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the block's acceleration.

Homework Equations

F=ma (Newton's Second Law)

The Attempt at a Solution

I got a and b by figuring out the equations T=F(g)sinx and F=F(g)cosx where F(g) is the force due to gravity. Part C is where I have the problem. I thought that because the rope was cut, the tension there would be 0 and thus the acceleration would be the tenstion

 

[Doc Al]

Part C is where I have the problem. I thought that because the rope was cut, the tension there would be 0 and thus the acceleration would be the tenstion

The tension is zero--the string no longer pulls on the block. Once the string is cut, what's the net force on the block? (What forces act on the block?)

 

[TS656577]

Right, that's what i figured. So wouldn't the net force be in the direction of opposite of the tension (ie in the picture, it would be F(g)sinx?)

 

[Doc Al]

Exactly! The only unbalanced force on the block is the component of gravity down the incline, which is $F_g \sin\theta$.

 

[TS656577]

Right, but since its an online program...i put in 7.71 and -7.71 and neither is right. The force due to gravity is 22.54 N and multiply that by sin20 = 7.71, but its apparently not right?

 

[Doc Al]

They want the acceleration, not the force. You're not done yet.

 

[TS656577]

So, since that's the force...F=ma? would you divide that by the mass then?

 

[Doc Al]

Right.