Determine the initial acceleration of the 15-kg block

In summary, the initial acceleration of the 15-kg block can be calculated by setting the sum of forces in the y-direction equal to 0 and solving for the normal force. For part (a), T = 23 N and for part (b), T = 26 N. The system is initially at rest with no slack in the cable, and the mass and friction of the pulleys are negligible. In solving for the normal force, the formula used is N = m*T*cos(30), but there may be an error in the calculation as the weight was not taken into account. The definition of normal force and the appropriate use of cos(30) should be clarified. Additionally, the value of "G" is not
  • #1
javii
23
0

Homework Statement


Determine the initial acceleration of the 15-kg block if (a) T = 23 N and (b) T = 26N. The system is initially at rest with no slack in the cable, and the mass and friction of the pulleys are negligible.
I have attached a picture of the problem.

The Attempt at a Solution


a)
I know, that there is a normal force, that I need to find.
I do that by setting the sum of forces in y-direction = 0
0=m*T*cos(30)+N
then I get N=0 ?
I don't think that is correct.
B)
I don't know how to solve this part either.
 

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  • #2
What's the definition of normal force?
 
  • #3
Where did you come up with mTcos30. That doesn't make sense to me. It doesn't make sense that you are multiplying mass times the tension and it doesn't make sense why you are using cos30. And you forgot one of the forces in y direction - the weight. But starting with summing forces in y direction is good. And then do x direction.

Edit: By the way, what is "G"?
 

1. What is meant by the term "initial acceleration"?

Initial acceleration refers to the rate at which an object's velocity changes at the very beginning of its motion. It is the acceleration at the start of a motion before any external forces act on the object.

2. How is the initial acceleration of a 15-kg block determined?

The initial acceleration of a 15-kg block can be determined by dividing the net force acting on the block by its mass. This is based on Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

3. What is the formula for calculating initial acceleration?

The formula for calculating initial acceleration is a = F/m, where "a" is the acceleration, "F" is the net force, and "m" is the mass of the object. This can also be written as a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time.

4. Can initial acceleration be negative?

Yes, initial acceleration can be negative. This indicates that the object is slowing down or accelerating in the opposite direction of its initial motion. For example, if a 15-kg block is initially moving to the right with a velocity of 10 m/s, and a net force of -20 N is applied to it, the initial acceleration would be -1.33 m/s², indicating that the block is slowing down in the right direction.

5. What units are used to measure initial acceleration?

Initial acceleration is typically measured in units of meters per second squared (m/s²) in the metric system, or in feet per second squared (ft/s²) in the imperial system. These units represent the change in velocity over time and are commonly used in physics and engineering.

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