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Setler [38]
3 years ago
12

A large box of mass M is moving on a horizontal floor at speed v0. A small box of mass m is sitting on top of the large box. The

coefficient of static friction between the two boxes is μs and coefficient of kinetic friction between the large box and floor is μk. Find an expression for the shortest distance dmin in which the large box can stop without the small box slipping.
Physics
1 answer:
gayaneshka [121]3 years ago
7 0

Answer:

dmin = V0^2 / {2(9.8)(μs)}

Explanation:

According to free body diagram, the only forces acting on the small box are force of gravity and force of friction.  

Therefore, the vector sum of the forces in the horizontal direction will be,

ma = F of friction which would be ma = mgμs

a = gμs ……. (1)

Kinematics equation states that, Vf^2 = Vi^2+ 2a (delta d)

Since the large box stops moving, which means Vf = 0 and initial velocity Vi=V0, then kinematics equation becomes

0 = V0^2 + 2a (delta d)

(delta d or dmin) = V0^2/2a …… (2)

 

Substitute the value of a from eqn.1 in eqn. 2, we should get

dmin = V0^2 / {2(9.8)(μs)}

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4 0
3 years ago
A pendulum has 294 J of potential energy at the highest point of its swing. How much kinetic energy will it have at the bottom o
baherus [9]

Newton's law of conservation states that energy of an isolated system remains a constant. It can neither be created nor destroyed but can be transformed from one form to the other.


Implying the above law of conservation of energy in the case of pendulum we can conclude that at the bottom of the swing the entire potential energy gets converted to kinetic energy. Also the potential energy is zero at this point.


Mathematically also potential energy is represented as


Potential energy= mgh


Where m is the mass of the pendulum.


g is the acceleration due to gravity


h is the height from the bottom z the ground.


At the bottom of the swing,the height is zero, hence the potential energy is also zero.


The kinetic energy is represented mathematically as


Kinetic energy= 1/2 mv^2


Where m is the mass of the pendulum


v is the velocity of the pendulum


At the bottom the pendulum has the maximum velocity. Hence the kinetic energy is maximum at the bottom.


Energy can neither be created e destroyed. It can only be transferred from one form to another. Implying this law and the above explainations we conclude that at the bottom of the pendulum,the potential energy=0 and the kinetic energy=294J as the entire potential energy is converted to kinetic energy at the bottom.



6 0
3 years ago
A pressure of 400 Pa is applied to an area of 2.5 m2.What force applies this pressure?
Irina-Kira [14]
F = 400 Pa x 2.5 m2
F = 1 kN
4 0
2 years ago
How long would it take an object to reach the ground from the top of a building that is 470 feet tall? Round to the nearest tent
Zinaida [17]

Answer:

It would take the object 5.4 s to reach the ground.

Explanation:

Hi there!

The equation of the height of a free-falling object at any given time, neglecting air resistance, is the following:

h = h0 + v0 · t + 1/2 · g · t²

Where:

h = height of the object at time t.

h0 = initial height.

v0 = initial velocity.

g = acceleration due to gravity (-32.2 ft/s² considering the upward direction as positive).

t = time

Let´s supose that the object is dropped and not thrown so that v0 = 0. Then:

h = h0 + 1/2 · g · t²

We have to find the time at which h = 0:

0 = 470 ft - 1/2 · 32.2 ft/s² · t²

Solving for t:

-470 ft = -16.1 ft/s² · t²

-470 ft / -16.1 ft/s² = t²

t = 5.4 s

3 0
3 years ago
How much force is required to accelerate a 22Kg mass at 6 m/s?
GuDViN [60]

Answer:

F = 132N

Explanation:

7 0
3 years ago
Read 2 more answers
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