Determine the magnitude of the maximum acceleration

In summary, the block has a mass of 0.677 kg and is attached to a horizontal spring with a spring constant of 88.6 N/m. When given a displacement of +0.170 m along the +x axis and then released from rest, the spring exerts a force of -15.062 N on the block. The resulting oscillatory motion has an angular frequency of 11.4399 rad/s, a maximum speed of 1.944 m/s, and a maximum acceleration of 0.044948 m/s^2. The relevant equations for this problem are F = -kx, angular freq = sq rt(k/m), and a = m/(kx).
  • #1
Kris1120
42
0

Homework Statement




A block of mass m = 0.677 kg is fastened to an unstrained horizontal spring whose spring constant is k = 88.6 N/m. The block is given a displacement of +0.170 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest. (a) What is the force (with sign) that the spring exerts on the block just before the block is released? (b) Find the angular frequency of the resulting oscillatory motion. (c) What is the maximum speed of the block? (d) Determine the magnitude of the maximum acceleration of the block.

Homework Equations



(a) F(applied) = kx
(b) angular freq = sq rt(k/m)
(c) (1/2)kx^2 = (1/2) mv^2
(d)a = m/(kx)


The Attempt at a Solution



(a) F = 88.6 n/m * 0.170 m = +15.062 N

(b) I got 11.4399 rad/s which was correct

(c) I got 1.944 m/s which was correct

(d) a = 0.677 kg / (88.6 N/m * 0.170 m) = 0.044948
 
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  • #2
Looks good. For (d), you could have just written a = F/m, and used your answer for max F from part (a).
 
  • #3
Hi Kris1120,

I think a couple of your relevant equations are incorrect, and is giving your wrong answers to part a and d.

Kris1120 said:

Homework Statement




A block of mass m = 0.677 kg is fastened to an unstrained horizontal spring whose spring constant is k = 88.6 N/m. The block is given a displacement of +0.170 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest. (a) What is the force (with sign) that the spring exerts on the block just before the block is released? (b) Find the angular frequency of the resulting oscillatory motion. (c) What is the maximum speed of the block? (d) Determine the magnitude of the maximum acceleration of the block.

Homework Equations



(a) F(applied) = kx

This is true if all they want is the magnitude; but here they want the sign. The correct formula (in terms of the vector F and vector x) is:

[tex]
\vec F = - k \vec x
[/tex]

(b) angular freq = sq rt(k/m)
(c) (1/2)kx^2 = (1/2) mv^2
(d)a = m/(kx)

This equation is not correct. You need to start by setting the expressions for the force magnitudes together, which is

[tex]
m a = k x
[/tex]

and then solve for a. What do you get for an answer?
 
  • #4
Yikes, that will teach me to pop in and try to help. Thanks for the corrections alphysicist.
 
  • #5
Ok so on part (a) it should be negative and on part (d) my equation was upside down! Thank you so much for your help!
 

What is the definition of "magnitude of the maximum acceleration"?

The magnitude of the maximum acceleration refers to the maximum rate of change of an object's velocity over a period of time. In other words, it measures how quickly an object's speed is changing at its fastest point.

How is the magnitude of the maximum acceleration calculated?

The magnitude of the maximum acceleration is calculated by dividing the change in an object's velocity by the time interval in which the change occurs. 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.

What units are used to measure the magnitude of the maximum acceleration?

The magnitude of the maximum acceleration is typically measured in meters per second squared (m/s²) in the metric system or feet per second squared (ft/s²) in the imperial system.

Can the magnitude of the maximum acceleration be negative?

Yes, the magnitude of the maximum acceleration can be negative. This indicates that the object is slowing down or changing direction in the opposite direction of its initial velocity.

How does the magnitude of the maximum acceleration relate to an object's motion?

The magnitude of the maximum acceleration is directly related to an object's motion. A larger magnitude of acceleration means the object is experiencing a greater change in velocity, resulting in faster or more dramatic motion. A smaller magnitude of acceleration means the object is experiencing a slower or less dramatic change in velocity.

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