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3 years ago

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A box rests on the (horizontal) back of a truck. The coefficient of static friction between the box and the surface on which it

rests is 0.24. What maximum distance can the truck travel (starting from rest and moving horizontally with constant acceleration) in 3.0 s without having the box slide?

1 answer:

vredina [299]3 years ago

3 0

Answer:

The distance is 11 m.

Explanation:

Given that,

Friction coefficient = 0.24

Time = 3.0 s

Initial velocity = 0

We need to calculate the acceleration

Using newton's second law

$F = ma$ ...(I)

Using formula of friction force

$F= \mu m g$ ....(II)

Put the value of F in the equation (II) from equation (I)

$ma=\mu mg$ ....(III)

$a = \mu g$

Put the value in the equation (III)

$a=0.24\times9.8$

$a=2.352\ m/s^2$

We need to calculate the distance,

Using equation of motion

$s = ut+\dfrac{1}{2}at^2$

$s=0+\dfrac{1}{2}2.352\times(3.0)^2$

$s=10.584\ m\ approx\ 11\ m$

Hence, The distance is 11 m.

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3) The frequency of the oscillation is C) 1.6 Hz

4) The period of vibration is B) 0.6 s

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Explanation:

1)

The period of a simple pendulum is given by

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From the equation, we see that the period of the pendulum depends only on its length and on the acceleration of gravity, while there is no dependence on the mass of the pendulum or on the amplitude of oscillation. Therefore, the correct option is

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2)

The angular acceleration of the rotating disc is given by the equation

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$\omega_i$ is the initial angular velocity

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For the compact disc in this problem we have:

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Substituting, we find

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For the oscillator in this problem, we have the following relationship

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which implies that

$\omega^2 = 100$

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Also, the angular frequency is related to the frequency $f$ by

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Therefore, the frequency of this simple harmonic oscillator is

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4)

When the mass is hanging on the sping, the weight of the mass is equal to the restoring force on the spring, so we can write

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k is the spring constant

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We can re-arrange the equation as

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According to the Pascal principle, the pressure on the two pistons is the same, so we can write

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So, the closest answer is B) 266.7 N.

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