Question

A crate pushed along the floor with velocity v⃗ i slides a distance d after the pushing force is removed. if the mass of the crate is doubled but the initial velocity is not changed, what distance does the crate slide before stopping?

Answer 1

Define
m = the  mass of the crate.
F = μmg, the resistive dynamic frictional force,
      where μ =dynamic coefficient of friction.
a =  the deceleration, when the crate slides subject only to to the frictional force.

The crate travels a distance d with initial velocity of v. Therefore
v² - 2ad = 0
a = v²/(2d)            (1)

Also,
F = ma
F  = (mv²)/(2d)     (2)

When m is doubled, then
F = (2mv²)/(2d) = (mv²)/d
The corresponding deceleration is
a = F/m = v²/d

Therefore, the new distance traveled, D, is given by
v² - 2(v²/d)D = 0
D = d/2
The new distance traveled is one half of d.

Answer: d/2.

Answer 2

If the mass of the crate is doubled but the initial velocity is not changed, the crate slides distance d before stopping.

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Further explanation

Let's recall the formula of Kinetic Energy as follows:

$\large {\boxed {E_k = \frac{1}{2}mv^2 }$

Ek = Kinetic Energy ( Newton )

m = Object's Mass ( kg )

v = Speed of Object ( m/s )

Let us now tackle the problem !

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Given:

initial height = h₁ = 26 m

final height = h₂ = 16 m

initial speed = v₁ = 0 m/s

coefficient of friction = μ

gravitational acceleration = g

distance = d

Asked:

final speed = v₂ = ?

Solution:

We will use Work and Energy formula to solve this problem as follows:

$W = \Delta Ek$

$-f d = Ek_{final} - Ek_{initial}$

$-\mu N d = \frac{1}{2}m (v_f)^2 - \frac{1}{2} m (v_i)^2$

$-\mu mg d = \frac{1}{2}m (v_f)^2 - \frac{1}{2} m (v_i)^2$

$-\mu mg d = \frac{1}{2}m (0)^2 - \frac{1}{2} m (v_i)^2$

$-\mu mg d = \frac{1}{2} m (v_i)^2$

$\mu g d = \frac{1}{2} (v_i)^2$

$d = \frac{1}{2} (v_i)^2 \div ( \mu g )$

$\boxed {d = \frac { (v_i)^2 } { 2 \mu g } }$

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From information above we can conclude that the distance is independent to the mass of the crate.

If the mass of the crate is doubled but the initial velocity is not changed, the crate slides the same distance d before stopping.

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441
• Newton's Law of Motion: brainly.com/question/10431582
• Example of Newton's Law: brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics