Find the magnitude of the block's acceleration

In summary: So now you have the magnitude of the acceleration.In summary, the task is to find the tension in a cord and the normal force acting on a block with a given mass and angle. Using Newton's Second Law, the equations T=F(g)sinx and F=F(g)cosx are used to calculate the tension and normal force. However, when the cord is cut, the tension becomes zero and the net force on the block is the component of gravity down the incline, which is F_g \sin\theta. Dividing this force by the mass of the block gives the magnitude of the acceleration.
  • #1
TS656577
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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
 

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  • #2
TS656577 said:
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?)
 
  • #3
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?)
 
  • #4
Exactly! The only unbalanced force on the block is the component of gravity down the incline, which is [itex]F_g \sin\theta[/itex].
 
  • #5
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?
 
  • #6
They want the acceleration, not the force. You're not done yet.
 
  • #7
So, since that's the force...F=ma? would you divide that by the mass then?
 
  • #8
Right.
 

Related to Find the magnitude of the block's acceleration

1. What is the definition of acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is measured in meters per second squared (m/s^2).

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. Can the magnitude of acceleration be negative?

Yes, the magnitude of acceleration can be negative. This indicates that the object is slowing down or changing direction.

4. How does the mass of an object affect its acceleration?

The mass of an object does not directly affect its acceleration. However, objects with larger masses may require more force to accelerate at the same rate as objects with smaller masses.

5. What factors can affect the magnitude of an object's acceleration?

The magnitude of an object's acceleration can be affected by the net force acting on the object, the mass of the object, and any external forces such as friction or air resistance.

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