Magnitude of Acceleration after initial impulse?

In summary, the magnitude of the acceleration of a block with mass 3.04 kg on an incline with an angle of 20.3° and coefficients of static and kinetic friction of 0.645 and 0.449 respectively, after an initial impulse sets it in motion downhill is -0.726 m/s^2. To find the acceleration when the block is traveling uphill, you need to identify the forces acting on the block and apply Newton's 2nd law. One of the forces has changed direction and therefore its sign, which needs to be taken into account in the calculations.
  • #1
jumpingjack90
14
0
Magnitude of Acceleration after initial impulse?

Homework Statement


A block with a mass of m = 3.04 kg is at rest on an incline. The angle of the incline is θ = 20.3° with respect to the horizontal. The coefficient of static friction between the object and the incline is μs = 0.645, the coefficient of kinetic friction is μk = 0.449.

a.) What would be the magnitude of the object's acceleration after an initial impulse set it in motion downhill on the incline?
b.)What would be the magnitude of the object's acceleration after an initial impulse set it in motion uphill on the incline?

Homework Equations


F=(uk)(mg)(cos(theta))
ma=mgsin(theta)-mg(uk)(cos(theta))

The Attempt at a Solution


I have no idea what to do. I tried using the above equations and found that
a=(3.04)(9.8)(sin(20.3))-(9.8)(3.04)(cos(20.3))(0.449) / (3.04) = -0.726 m/s^2 which is the wrong answer. ?
 
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  • #2


jumpingjack90 said:
I tried using the above equations and found that
a=(3.04)(9.8)(sin(20.3))-(9.8)(3.04)(cos(20.3))(0.449) / (3.04) = -0.726 m/s^2 which is the wrong answer. ?
Looks OK to me. Are you sure you gave the magnitude of the acceleration?
 
  • #3


ok. found the answer to part 1. How do you do part 2 when the block is traveling uphill?
 
  • #4


jumpingjack90 said:
How do you do part 2 when the block is traveling uphill?
Identify the forces acting on the block, then apply Newton's 2nd law. (That's how you should solve part 1 as well. That way you know how to derive the formula for acceleration.)
 
  • #5


What Doc is saying is, if you look at the forces involved, one of them has changed its direction and therefore its sign. If you just try to plug into equations you were given, you won't see that.
 

1. What is the definition of magnitude of acceleration after an initial impulse?

The magnitude of acceleration after an initial impulse is the measure of how much an object's velocity changes in a given amount of time due to an external force or impulse.

2. How is the magnitude of acceleration after an initial impulse calculated?

The magnitude of acceleration can be calculated by dividing the change in velocity by the time it takes for the change to occur. This can be represented by the equation a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What factors affect the magnitude of acceleration after an initial impulse?

The magnitude of acceleration after an initial impulse is affected by the mass and velocity of the object, as well as the force and duration of the impulse. The direction of the force also plays a role in determining the direction of the acceleration.

4. How does the magnitude of acceleration after an initial impulse relate to Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Therefore, the greater the force or the smaller the mass, the greater the magnitude of acceleration after an initial impulse.

5. Can the magnitude of acceleration after an initial impulse be negative?

Yes, the magnitude of acceleration after an initial impulse can be negative. This indicates that the object is decelerating or slowing down due to the force acting in the opposite direction of its motion.

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