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alekssr [168]
3 years ago
5

A 1445-kg car,c, moving east at 21.2m/s, collides with a 2625-kg car,d,moving south at 17.5 m/s, and the cars stick together. In

what direction and with what speed do they move after the collision
Physics
1 answer:
Vitek1552 [10]3 years ago
6 0

Answer:

<em>After the collision, they move with a speed of 13.57 m/s at 56.30° south of east</em>

Explanation:

<u>Conservation Of Momentum </u>

The total momentum of a system of particles with masses m1,m2,...mn that interact without the action of external forces, is conserved. It means that, being \vec P and \vec P' the initial  and final momentums respectively:

\vec P = \vec P'

Or equivalently, for a two-mass system

m_1\vec v_1+m_2\vec v_2=m_1\vec v_1'+m_2\vec v_2'

All the velocities are vectors. Let's express the velocities in magnitude v and direction \theta as (v,\theta). It's rectangular components will be

v_x=vcos\theta

v_y=vsin\theta

The first car is moving east at 21.2 m/s. Its velocity is

\vec v_1=(21.2,0^o)

Recall that East is the zero-degree reference for angles

Expressing in rectangular form:

\vec v_1==

The second car is moving south at 17.5 m/s. Its velocity is

\vec v_2=(17.5,270^o)

\vec v_2==

The total initial momentum is

\vec P=m_1\vec v_1+m_2\vec v_2

\vec P=1445+2625

\vec P=\ Kg.m/s

They collide and stick together in a common mass and velocity \vec v', thus

\vec P'=(m_1+m_2)\vec v'

It must be equal to the initial momentum, thus

(m_1+m_2)\vec v'=\ Kg.m/s

Solving for \vec v'

\displaystyle \vec v'=\frac{\ Kg.m/s}{m_1+m_2}

\displaystyle \vec v'=\frac{\ Kg.m/s}{4070}

\displaystyle \vec v'=\ m/s

The magnitude of \vec v' is

|\vec v'|=\sqrt{7.53^2+(-11.29)^2}=13.57\ m/s

The direction angle is

\displaystyle tan\theta=\frac{-11.29}{7.53}

\displaystyle \theta=-56.30^o

After the collision, they move with a speed of 13.57 m/s at 56.30° south of east

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pashok25 [27]

Answer:

1. D

2. D

3. A

The reason why your body goes right and the car car goes left is because your body tries to stay where it was, which is on the right. Your upper body doesn't feel a force and because of that continues in the same direction. Your lower half is pulled out from under you by seat friction to the left, leaving you leaning to the right.

8 0
2 years ago
Consider a cyclotron in which a beam of particles of positive charge q and mass m is moving along a circular path restricted by
Ulleksa [173]

A) v=\sqrt{\frac{2qV}{m}}

B) r=\frac{mv}{qB}

C) T=\frac{2\pi m}{qB}

D) \omega=\frac{qB}{m}

E) r=\frac{\sqrt{2mK}}{qB}

Explanation:

A)

When the particle is accelerated by a potential difference V, the change (decrease) in electric potential energy of the particle is given by:

\Delta U = qV

where

q is the charge of the particle (positive)

On the other hand, the change (increase) in the kinetic energy of the particle is (assuming it starts from rest):

\Delta K=\frac{1}{2}mv^2

where

m is the mass of the particle

v is its final speed

According to the law of conservation of energy, the change (decrease) in electric potential energy is equal to the increase in kinetic energy, so:

qV=\frac{1}{2}mv^2

And solving for v, we find the speed v at which the particle enters the cyclotron:

v=\sqrt{\frac{2qV}{m}}

B)

When the particle enters the region of magnetic field in the cyclotron, the magnetic force acting on the particle (acting perpendicular to the motion of the particle) is

F=qvB

where B is the strength of the magnetic field.

This force acts as centripetal force, so we can write:

F=m\frac{v^2}{r}

where r is the radius of the orbit.

Since the two forces are equal, we can equate them:

qvB=m\frac{v^2}{r}

And solving for r, we find the radius of the orbit:

r=\frac{mv}{qB} (1)

C)

The period of revolution of a particle in circular motion is the time taken by the particle to complete one revolution.

It can be calculated as the ratio between the length of the circumference (2\pi r) and the velocity of the particle (v):

T=\frac{2\pi r}{v} (2)

From eq.(1), we can rewrite the velocity of the particle as

v=\frac{qBr}{m}

Substituting into(2), we can rewrite the period of revolution of the particle as:

T=\frac{2\pi r}{(\frac{qBr}{m})}=\frac{2\pi m}{qB}

And we see that this period is indepedent on the velocity.

D)

The angular frequency of a particle in circular motion is related to the period by the formula

\omega=\frac{2\pi}{T} (3)

where T is the period.

The period has been found in part C:

T=\frac{2\pi m}{qB}

Therefore, substituting into (3), we find an expression for the angular frequency of motion:

\omega=\frac{2\pi}{(\frac{2\pi m}{qB})}=\frac{qB}{m}

And we see that also the angular frequency does not depend on the velocity.

E)

For this part, we use again the relationship found in part B:

v=\frac{qBr}{m}

which can be rewritten as

r=\frac{mv}{qB} (4)

The kinetic energy of the particle is written as

K=\frac{1}{2}mv^2

So, from this we can find another expression for the velocity:

v=\sqrt{\frac{2K}{m}}

And substitutin into (4), we find:

r=\frac{\sqrt{2mK}}{qB}

So, this is the radius of the cyclotron that we must have in order to accelerate the particles at a kinetic energy of K.

Note that for a cyclotron, the acceleration of the particles is achevied in the gap between the dees, where an electric field is applied (in fact, the magnetic field does zero work on the particle, so it does not provide acceleration).

6 0
3 years ago
A broom with a long handle balances at its centre of gravity as shown in the figure. If you cut the broom into two parts through
pantera1 [17]

Answer:

c) Both the parts will weigh the same

Explanation:

center of gravity is based on weight so if you cut down the center of gravity you would have 2 equal parts

(might be D if it is cutting against the center of gravity)

6 0
3 years ago
A gas in a cylinder expands from a volume of 0.110 m³ to 0.320 m³. heat flows into the gas just rapidly enough to keep the press
Elden [556K]

80000 Joule is the change in the internal energy of the gas.

<h3>In Thermodynamics, work done by the gas during expansion at constant pressure:</h3>

ΔW = -pdV

ΔW = -pd (V₂ -V₁)

ΔW = - 1.65×10⁵ pa (0.320m³ - 0.110m³)

     = - 0.35×10⁵ pa.m³

     = - 35000 (N/m³)(m³)

     = -35000 Nm

ΔW = -35000 Joule

Therefore, work done by the system = -35000 Joule

<h3>Change in the internal energy of the gas,</h3>

ΔV = ΔQ + ΔW

Given:

ΔQ = 1.15×10⁵ Joule

ΔW = -35000 Joule

ΔU = 1.15×10⁵ Joule - 35000 Joule

      = 80000 Joule.

Therefore, the change in the internal energy of the gas= 80000 Joule.

Learn more about thermodynamics here:

brainly.com/question/14265296

#SPJ4

3 0
2 years ago
Boxes are transported from one location to another in a warehouse by means of a conveyor belt that moves with a constant speed o
krek1111 [17]

Answer:

P = 15.90 W

Explanation:

given,

speed of conveyor belt = 0.56 m/s

conveyor belt move up to = 2 m      

angle made with the horizontal = 15°

mass of the box = 2.1 kg                      

rate is the force of the conveyor belt doing work on the box as the box moves up                                                  

P = F v cos ∅

P = 3 × 9.8 × 0.56 × cos 15°

P = 15.90 W

6 0
3 years ago
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