A bullet of mass 0.01 kg moving horizontally strikes a block of wood of mass 1.5 kg which is suspended as a pendulum. The bullet lodges in the wood, and together they swing upwards a distance of 0.40 m. What was the velocity of the bullet just before it struck the wooden block

Answers

Answer 1

Answer:

Answer:

423m/s

Explanation:

Suppose after the impact, the bullet-block system swings upward a vertical distance of 0.4 m. That's means their kinetic energy is converted to potential energy:

$E_p = E_k$

$mgh = mv^2/2$

where m is the total mass and h is the vertical distance traveled, v is the velocity right after the impact at, which we can solve by divide both sides my m

Let g = 9.81 m/s2

$gh = v^2/2$

$v^2 = 2gh = 2 * 9.81* 0.4 = 7.848$

$v = √(7.848) = 2.8m/s$

According the law of momentum conservation, momentum before and after the impact must be the same

$m_uv_u + m_ov_o = (m_u + m_o)v$

where $m_u = 0.01, v_u$ are the mass and velocity of the bullet before the impact, respectively. $m_ov_o$ are the mass and velocity of the block before the impact, respectively, which is 0 because the block was stationary before the impact

$0.01v_u + 0 = (0.01 + 1.5)*2.8$

$0.01v_u = 4.23$

$v_u = 4.23 / 0.01 = 423 m/s$

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An object of mass m swings in a horizontal circle on a string of length L that tilts downward at angle θ.Find an expression for the angular velocity ω in terms of g, L and angle θ.

Answers

Answer:

The expression would be ω = $\sqrt{(g)/(L sin 0 ) }$

Explanation:

Given that ω is the angular velocity

g is the acceleration due to gravity

L is the length

θ is the angle of downward tilt

For an object we compare the horizontal and vertical component of the forces acting on the body;

For vertical component

T sinθ = mg............1

For the horizontal component

T cos θ = $(mv^(2) )/(R)$ .............2

R is our radius and is = L cos θ

v = ωR

substituting into equation 2 we have

T cos θ = m(ωR $)^(2)$ /R

T cos θ=m(ω $)^(2)$ R ..................3

Now comparing the vertical and the horizontal component we have;

equation 1 divided by equation 3 we have

T sin θ /T cos θ = mg / m(ω $)^(2)$ R

Tan θ = g / (ω $)^(2)$ R............4

Making ω the subject formula we have;

(ω $)^(2)$ = g/ R Tan θ

But R = L cos θ and Tan θ = sin θ/ cosθ

putting into equation 4 we have;

(ω $)^(2)$ = g /[( L cos θ) x( sin θ/ cosθ)]

(ω $)^(2)$ = g/ L sinθ

ω = $\sqrt{(g)/(L sin 0 ) }$

Therefor the expression for the angular velocity ω in terms of g, L and angle θ would be ω = $\sqrt{(g)/(L sin 0 ) }$

Let g, r, L and T are gravity, radius, length, and angle of string w/r/t vertical, respectively.
Then
ω²r = rg/Lcos T
ω² = g/L cos T
ω = √(g / L cos T)

How can scientific method solve real world problems examples

Answers

The scientific method is nothing more than a process for discovering answers. While the name refers to “science,” this method of problem solving can be used for any type of problem

) An electron moving along the x-axis enters a magnetic field. If the electron experiences a magnetic deflection in the -y direction, what is the direction of the magnetic field in this region

Answers

Answer:

- z direction

Explanation:

To find the direction of the magnetic field, you take into account that the magnetic force over a charge, is given by the following cross product:

$\vec{F_B}=q\vec{v}\ X\ \vec{B}$ (1)

F_B: magnetic force

q: charge of the particle

v: velocity of the charge

B: magnetic field

In this case you have that the electron is moving along x-axis. You can consider this direction as the ^i direction. The electron experiences a magnetic deflection in the -y direction, that is, in the -^j direction.

By the cross products between unit vectors, you have that:

-^j = ^i X ^k

That is, the cross product between two vectors, one in the +x direction, and another one in the +z direction, generates a vector in the -y direction. However, it is necessary to take into account that the negative charge of the electron change the sign of the result of the cross product, which demands that the second vector is in the -z direction. That is:

-^i X -k^ = ^i X ^k = - ^j

Hence, the direction of the magnetic field is in the -z direction

How does the force of gravity change as the mass of one object doubles?

Answers

The force of gravity changes as the mass of one object doubles. As the mass of one object is doubled then the force between the objects also gets doubled.

What is Force?

Force is an influence which can change the motion of an object through the application of an external force. A force can cause an object with the mass to change its velocity, that is the object undergo acceleration.

Force is directly proportional to the mass of the object and the acceleration of the object. If we double the mass of one of the objects, then we double the strength of the force. If we double the masses of both the objects, then we quadruple the strength of force.

Learn more about Force here:

brainly.com/question/13191643

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If the mass of one of the objects is doubled, then the force of gravity between them is doubled. ... Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.

When you walk at an average speed (constant speed, no acceleration) of 24 m/s in 94.1 secyou will cover a distance of__?

Answers

Answer:

2258.4 m

Explanation:

Distance covered is a product of speed and time hence

s=vt where s is the displacement/distance covered, v is the speed and t is the time taken

s=24*94.1=2258.4 m

Therefore, the distance covered is 2258.4 m

The brakes of a car moving at 14m/s are applied, and the car comes to a stop in 4s. (a) What was the cars acceleration? (b) How long would the car take to come to a stop starting from 20m/s with the same acceleration? (c) How long would the car take to slow down from 20m/s to 10m/s with the same acceleration?