Solve Impulsive Motion Problem: Initial Velocity 9m/s, uk=.3, Theta=20 Deg

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In summary, using the Principle of Impulse and Momentum, the time taken for block A to reach zero velocity is 1.47 seconds when the angle is 20 degrees. This method was also used for finding the time when the angle is 0 degrees, which resulted in 3.06 seconds. However, there may be a mistake in the problem as the book's answer for part (a) is 0.306 or 3.06 seconds.
  • #1
VSCCEGR
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Problem:

The initial velocity of block A is 9m/s. Knowing that uk=.3 Determine the time for the block to reach zero velocity. When (theta)=20 deg.

Here is my work so far.

mv_1+Imp_1,2=mv_2

Imp_1,2=Ff(t)+sin(theta)W(t)
Ff=Cos(theta)uk(mg)
W=mg
Imp=9.81cos(20).3m+9.81sin(20)m
Imp=6.12mt

9m+6.12mt=0
t=1.47s


This answer is Wrong It Should Be .963s

What Have I Missed?
 
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  • #2
Strange, i get the exact same answer 1.47

marlon
 
  • #3
[tex]v_x = v_i -g(0.3cos(20)+sin(20))t[/tex]
[tex]v_y = 0[/tex]

X is along the incline and y perpendicular to it. I get the same answer using a different approach. Are you sure it's not 1.47 ?

marlon
 
  • #4
Yes, I did place the positive x-axis in the direction of movement, but it really should not matter because I am using the Principle of Impulse and Momentum.
(a) part was finding the time taken if (theta)=0deg. (3.06s I got this one right)
So I know my method works. There is just something I am missing.

The problem is from Beer and Johnston;
VECTOR MECHANICS for ENGINEERS:STATICS and DYNAMICS 7th Ed.
problem 13.124
For anyone who knows the book. (They may have made a mistake but i doubt it.)
 
Last edited:
  • #5
The answer for part (a) is .306 or is is 3.06?
 
  • #6
My bad, 3.06s
 
  • #7
OK, so for 0 degrees I get 3.06 s

and for 20 degrees I get 1.47 s

I think the book is wrong
 
  • #8
If you take the angle to be zero, my method also gives 3.06, just plug in that value into the equation for v_x

marlon

ps : i think there must be a mistake here. Perhaps someone else can double check this problem ?

Dexter, Doc Al, what do you get ??
 
  • #9
marlon said:
Dexter, Doc Al, what do you get ??

1.47s is correct. Using "impulse/momentum" is a perfectly OK way to solve this problem; it is equivalent to finding the acceleration and then using kinematics.
 
Last edited:

Related to Solve Impulsive Motion Problem: Initial Velocity 9m/s, uk=.3, Theta=20 Deg

1. What is impulsive motion?

Impulsive motion is a type of motion where an object experiences a sudden change in velocity due to an external force acting on it. This change in velocity is known as an impulse, and it can cause the object to move in a different direction or at a different speed.

2. How do you solve an impulsive motion problem?

To solve an impulsive motion problem, you need to use the equations of motion and the principles of mechanics. These equations and principles allow you to calculate the initial and final velocities, as well as the distance traveled by the object.

3. What is initial velocity?

Initial velocity is the velocity of an object at the beginning of its motion. It is usually denoted by the symbol "u" or "v0". In this problem, the initial velocity is given as 9m/s.

4. What is the coefficient of kinetic friction (uk)?

The coefficient of kinetic friction (uk) is a measure of the amount of friction between two surfaces when one is in motion. It is a dimensionless quantity and its value depends on the nature of the two surfaces in contact. In this problem, the value of uk is given as 0.3.

5. What is the role of Theta in solving an impulsive motion problem?

Theta (θ) represents the angle at which the force acts on the object. In an impulsive motion problem, it is important to consider the direction of the force and its angle of application in order to accurately calculate the final velocity and displacement of the object.

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