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lianna [129]
3 years ago
9

By calculating numerical quantities for a multiparticle system, one can get a concrete sense of the meaning of the relationships

Physics
1 answer:
damaskus [11]3 years ago
3 0

Answer:

Explanation:

Given that,

Stiffness K=460N/m

Extension e=0.37m

Two balls attached to a string

First ball has mass and velocity

M1 =8kg and V1~ =4i +11j +0k

For the second ball

M2 =4kg and V2~ =-3i+10j +0k

a. Momentum of system?

Momentum is given as

P = m1•V1~ +m2•V2~

P= 8(4i +11j +0k) +4(-3i+10j +0k)

P=32i + 88j + 0k -12i +40j + 0k

P= 20i + 128j + 0k kgm/s

2. Magnitude of each velocity is given as

V1²=Vx² +Vy² + Vz²

V1² =4²+11²+0²

V1² =137

V1 =√137

V1=11.705m/s

Also V2

V2²= Vx² +Vy² +Vz²

V2²=(-3)²+(10)² +0²

V2²=109

V2 = √109

V2 =10.44m/s

Ktot= k(trans) +k(rel)

d. K(trans) =½m1•V1²

K(trans) =½×8×11.705²

K(trans) = 548.03J

e. K(rel) =½m2•V2²

K(rel) =½ ×4×10.44²

K(rel) = 217.99J

c. Then, K(tot)=K(trans)+k(rel)

K(tot) =548.03+217.99

K(tot) = 766.02J

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A 190 g glider on a horizontal, frictionless air track is attached to a fixed ideal spring with force constant 160 N/m. At the i
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(a) Let <em>x</em> be the maximum elongation of the spring. At this point, the glider would have zero velocity and thus zero kinetic energy. The total work <em>W</em> done by the spring on the glider to get it from the given point (4.00 cm from equilibrium) to <em>x</em> is

<em>W</em> = - (1/2 <em>kx</em> ² - 1/2 <em>k</em> (0.0400 m)²)

(note that <em>x</em> > 4.00 cm, and the restoring force of the spring opposes its elongation, so the total work is negative)

By the work-energy theorem, the total work is equal to the change in the glider's kinetic energy as it moves from 4.00 cm from equilibrium to <em>x</em>, so

<em>W</em> = ∆<em>K</em> = 0 - 1/2 <em>m</em> (0.835 m/s)²

Solve for <em>x</em> :

- (1/2 (160 N/m) <em>x</em> ² - 1/2 (160 N/m) (0.0400 m)²) = -1/2 (0.190 kg) (0.835 m/s)²

==>   <em>x</em> ≈ 0.0493 m ≈ 4.93 cm

(b) The glider attains its maximum speed at the equilibrium point. The work done by the spring as it is stretched away from equilibrium to the 4.00 cm position is

<em>W</em> = - 1/2 <em>k</em> (0.0400 m)²

If <em>v</em> is the glider's maximum speed, then by the work-energy theorem,

<em>W</em> = ∆<em>K</em> = 1/2 <em>m</em> (0.835 m/s)² - 1/2 <em>mv</em> ²

Solve for <em>v</em> :

- 1/2 (160 N/m) (0.0400 m)² = 1/2 (0.190 kg) (0.835 m/s)² - 1/2 (0.190 kg) <em>v</em> ²

==>   <em>v</em> ≈ 1.43 m/s

(c) The angular frequency of the glider's oscillation is

√(<em>k</em>/<em>m</em>) = √((160 N/m) / (0.190 kg)) ≈ 29.0 Hz

3 0
2 years ago
The change in momentum of an object is equal to the ____________ that acts on it.
meriva

Answer : The change in momentum of an object is equal to the impulse that acts on it.

Explanation :

Change in momentum : The change in momentum of an object is the product of the mass and the change in velocity of an object.

The formula of change in momentum is,

\Delta p=m\times \Delta v

Impulse : An impulse of an object is the product of the force applied on an object and the change in time. Impulse is also equivalent to the change in momentum of  an object.

J=F\times \Delta t

Proof :

J=F\times \Delta t\\\\J=(m\times a)\times \Delta t\\\\J=m\times (a\times \Delta t)\\\\J=m\times \Delta v=\Delta p

Hence, the change in momentum of an object is equal to the impulse that acts on it.

3 0
3 years ago
Read 2 more answers
Does the gas have a well defined structure
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What gas? Gas is an invisible form so I don't see how it would have a "defined structure".

6 0
3 years ago
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Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 1012 W) pu
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Answer:

the best way to prevent cancer is to eat right

Explanation:

4 0
3 years ago
An 3.7 lb hammer head, traveling at 5.8 ft/s strikes a nail and is brought to a stop in 0.00068 s. The acceleration of gravity i
CaHeK987 [17]

Answer:

31677.2 lb

Explanation:

mass of hammer (m) = 3.7 lb

initial velocity (u) = 5.8 ft/s

final velocity (v) = 0

time (t) = 0.00068 s

acceleration due to gravity (g) 32 ft/s^{2}

force = m x ( a + g )

where

  • m is the mass = 3.7 lb
  • g is the acceleration due to gravity = 32 ft/s^{2}
  • a is the acceleration of the hammer

       from v = u + at

       a = (v-u)/ t

       a = (0-5.8)/0.00068 = -8529.4 ( the negative sign showa the its decelerating)

we can substitute all required values into force= m x (a+g)

force = 3.7 x (8529.4 + 32) = 31677.2 lb

       

4 0
3 years ago
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