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OleMash
2 months ago
13

A stationary 1.67-kg object is struck by a stick. The object experiences a horizontal force given by F = at - bt2, where t is th

e time in milliseconds from the instant the stick first contacts the object.
If :

a = 1500 N/(ms)

b = 20 N/(ms)2

what is the speed of the object just after it comes away from the stick at t = 2.74 ms?
Physics
1 answer:
serg [3.5K]2 months ago
5 0

Answer:

v_{f}  = 3289.8 m/s

Explanation:

This problem can be approached using momentum definitions.

     I = ∫ F dt

We substitute and compute.

     I = ∫ (at - bt²) dt

Integrating gives us:

      I = a t² / 2 - b t³ / 3

We will evaluate between the limits I=0 for t = 0 ms and higher I=I for t = 2.74 ms:

      I = a (2.74² / 2- 0) - b (2.74³ / 3 -0)

      I = a 3.754 - b 6.857

Substituting the values for a and b, we find:

      I = 1500 3.754 - 20 6.857

      I = 5,631 - 137.14

      I = 5493.9 N s

Next, we engage the relationship between impulse and momentum:

      I = Δp = m v_{f} - m v₀o

      I = m v_{f} - 0

     v_{f}  = I / m

    v_{f}  = 5493.9 /1.67

    v_{f}  = 3289.8 m/s

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