A metallic laboratory spring is typically 5.00 cm long and 0.150 cm in diameter and has 50 coils.

A block of mass M on a horizontal surface is connected to the end of a massless spring of spring constant k. The block is pulled

slamgirl [31]

Answer:

Minimum coefficient of kinetic friction between the surface and the block is $\mu_k=\frac{kx}{2Mg}$ .

Explanation:

Given:

Mass of the block = M

Spring constant = k

Distance pulled = x

According to the question:

We have to find the minimum co-efficient of kinetic friction between the surface and the block that will prevent the block from returning to its equilibrium with non-zero speed.

So,

From the FBD we can say that:

⇒ Normal force, $N=Mg$ ...equation(i)

⇒ Elastic potential energy, $PE$ = $\frac{kx^2}{2}$ ...equation (ii)

⇒ Frictional force, $f$ = $\mu_kN$ ...equation (iii)

⇒ Plugging (i) in (iii).

⇒ $f=\mu_kMg$

Now,

⇒ As we know that the energy lost due to friction is equivalent to PE .

⇒ $PE=fx$ ...considering PE as $mgh$ or $f(x)$ .

Arranging the equation.

⇒ $\frac{kx^2}{2}=\mu_k Mg (x)$

⇒ $\frac{kx}{2}=\mu_k Mg$ ...eliminating x from both sides.

⇒ $\frac{kx}{2Mg}=\mu_k$ ...dividing both sides wit Mg.

Minimum coefficient of kinetic friction between the surface and the block is $\frac{kx}{2Mg}=\mu_k$ .

4 0

4 years ago

If you fired a rifle straight upwards at 1000 m/s, how far up will the bullet get?

nadya68 [22]

Answer:

h = 51020.40 meters

Explanation:

Speed of the rifle, v = 1000 m/s

Let h is the height gained by the bullet. It can be calculated using the conservation of energy as :

$\dfrac{1}{2}mv^2=mgh$

$h=\dfrac{v^2}{2g}$

$h=\dfrac{(1000\ m/s)^2}{2\times 9.8\ m/s^2}$

h = 51020.40 meters

So, the bullet will get up to a height of 51020.40 meters. Hence, this is the required solution.

4 0

3 years ago

A 0.500 kg football is thrown with a speed of 15.0 m/s. A stationary receiver catches the ball and brings it to rest in 0.020 s.

Marizza181 [45]

Answer:

$Imp = 7.5\,\frac{kg\cdot m}{s}$

Explanation:

Let assume that direction is positive when football travels to the player. The situation can be described properly by applying the definition of Momentum and Impulse Theorem. That is to say:

$(0.5\,kg)\cdot (15\,\frac{m}{s}) - F \cdot (0.02\,s) = 0\,kg\cdot \frac{m}{s}$

The average force needed to stop is obtained after some algebraic manipulations:

$F = 375\,N$

The impulse delivered to the ball is:

$Imp = (375\,N)\cdot (0.02\,s)$

$Imp = 7.5\,\frac{kg\cdot m}{s}$

3 0

3 years ago

Read 2 more answers

Sound waves that enter the external acoustic meatus eventually encounter the __________, which then vibrates at the same frequen

7nadin3 [17]

Answer:

tympanic membrane (eardrum)

Explanation:

The sound waves spread through the air and reach the outer ear, into which they penetrate through the ear canal. In doing so, they stimulate the eardrum, which closes the inner end of the duct. By vibrating this membrane, the vibration of a chain of ossicles located in the middle ear is induced. These ossicles transmit their vibration to the oval window, which is a membranous structure that communicates the middle ear with the cochlea of the inner ear. When the oval membrane moves, it moves the liquid (perilymph) that fills one of the three cavities of the cochlea generating waves in it. These waves mechanically stimulate the sensory cells (hair cells) located in the organ of Corti, within the cochlea in the central cavity, the middle ramp. This cavity is filled with a liquid rich in K +, endolymph. The cells embedded in the endolymph, change their permeability to K + due to the movement of the cilia and respond by releasing a neurotransmitter that excites the nerve terminals, which initiate the auditory sensory pathway.

3 0

3 years ago

1. What are the ways that scientists answer questions and

Olegator [25]

Answer:

C. observations

Explanation:

a scientist have to observe somethng to find the answers or solve problems

5 0

3 years ago