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olchik [2.2K]
2 years ago
14

Block 1 (mass 2.00 kg) is moving rightward at 10.0 m/s and block 2 (mass 5.00 kg) is moving rightward at 3.00 m/s. The surface i

s frictionless, and a spring with a spring constant of 1120 N/m is fixed to block 2. When the blocks collide, the compression ofthe spring is maximum at the instant the blocks have the same velocity. (a) Find the maximum compression.(b) Find the final velocities of the two blocks.
Physics
1 answer:
DaniilM [7]2 years ago
5 0

Answer:

a) 0.25m

b) 5 m/s

Explanation:

When the spring is compressed both boxes are moving with the same velocity, so applying the principle of linear momentum conservation:

m1*v_{o1}+m2*v_{o2}=(m1+m2)*v\\v=5m/s

Now applying the principle of energy conservation:

K1+K2+U_{g1}-U_e=Kf+U_{g2}\\K1+0-U_e=K2+0\\U_e=K1+K2-kf\\\frac{1}{2}*k*x^2+=\frac{1}{2}*m1*v1^2+\frac{1}{2}*m1*v1^2-\frac{1}{2}*(m1+m2)*v^2\\\\x=\sqrt{\frac{2.00kg*(10m/s)^2+5.00kg*(3.00m/s)^2-7.00kg*(5m/s)^2}{1120N/m}}\\x=0.25m

We got that the maximum compression is 0.25m.

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A person throws a stone from the corner edge of a building. The stone's initial velocity is 28.0 m/s directed at 43.0° above the
Naya [18.7K]

The stone's acceleration, velocity, and position vectors at time t are

\mathbf a(t)=-g\,\mathbf j

\mathbf v(t)=v_{i,x}\,\mathbf i+\left(v_{i,y}-gt\right)\,\mathbf j

\mathbf r(t)=v_{i,x}t\,\mathbf i+\left(y_i+v_{i,y}t-\dfrac g2t^2\right)\,\mathbf j

where

g=9.80\dfrac{\rm m}{\mathrm s^2}

v_{i,x}=\left(28.0\dfrac{\rm m}{\rm s}\right)\cos43.0^\circ\approx20.478\dfrac{\rm m}{\rm s}

v_{i,y}=\left(28.0\dfrac{\rm m}{\rm s}\right)\sin43.0^\circ\approx19.096\dfrac{\rm m}{\rm s}

and y_i is the height of the building and initial height of the rock.

(a) After 6.1 s, the stone has a height of 5 m. Set the vertical component (\mathbf j) of the position vector to 5 m and solve for y_i:

5\,\mathrm m=y_i+\left(19.096\dfrac{\rm m}{\rm s}\right)(6.1\,\mathrm s)-\dfrac12\left(9.80\dfrac{\rm m}{\mathrm s^2}\right)(6.1\,\mathrm s)^2

\implies\boxed{y_i\approx70.8\,\mathrm m}

(b) Evaluate the horizontal component (\mathbf i) of the position vector when t=6.1\,\mathrm s:

\left(20.478\dfrac{\rm m}{\rm s}\right)(6.1\,\mathrm s)\approx\boxed{124.92\,\mathrm m}

(c) The rock's velocity vector has a constant horizontal component, so that

v_{f,x}=v_{i,x}\approx20.478\dfrac{\rm m}{\rm s}

where v_{f,x}

For the vertical component, recall the formula,

{v_{f,y}}^2-{v_{i,y}}^2=2a\Delta y

where v_{i,y} and v_{f,y} are the initial and final velocities, a is the acceleration, and \Delta y is the change in height.

When the rock hits the ground, it will have height y_f=0. It's thrown from a height of y_i, so \Delta y=-y_i. The rock is effectively in freefall, so a=-g. Solve for v_{f,y}:

{v_{f,y}}^2-\left(19.096\dfrac{\rm m}{\rm s}\right)^2=2(-g)(-124.92\,\mathrm m)

\implies v_{f,y}\approx-53.039\dfrac{\rm m}{\rm s}

(where we took the negative square root because we know that v_{f,y} points in the downward direction)

So at the moment the rock hits the ground, its velocity vector is

\mathbf v_f=\left(20.478\dfrac{\rm m}{\rm s}\right)\,\mathbf i+\left(-53.039\dfrac{\rm m}{\rm s}\right)\,\mathbf j

which has a magnitude of

\|\mathbf v_f\|=\sqrt{\left(20.478\dfrac{\rm m}{\rm s}\right)^2+\left(-53.039\dfrac{\rm m}{\rm s}\right)^2}\approx\boxed{56.855\dfrac{\rm m}{\rm s}}

(d) The acceleration vector stays constant throughout, so

\mathbf a(t)=\boxed{-g\,\mathbf j}

4 0
2 years ago
How often do you rely on media for scientific information to make decisions in your life? (No weather answer please)
vodka [1.7K]
The majority of the time


6 0
2 years ago
Read 2 more answers
Water is boiled at sea level in a coffeemaker equipped with an immersion-type electric heating element. The coffee maker contain
Luden [163]

Answer:

P=1362\ W

t'=251.659\ s is time required to heat to boiling point form initial temperature.

Explanation:

Given:

initial temperature of water, T_i=18^{\circ}C

time taken to vapourize half a liter of water, t=18\ min=1080\ s

desity of water, \rho=1\ kg.L^{-1}

So, the givne mass of water, m=1\ kg

enthalpy of vaporization of water, h_{fg}=2256.4\times 10^{-3}\ J.kg^{-1}

specific heat of water, c=4180\ J.kg^{-1}.K^{-1}

Amount of heat required to raise the temperature of given water mass to 100°C:

Q_s=m.c.\Delta T

Q_s=1\times 4180\times (100-18)

Q_s=342760\ J

Now the amount of heat required to vaporize 0.5 kg of water:

Q_v=m'\times h_{fg}

where:

m'=0.5\ kg= mass of water vaporized due to boiling

Q_v=0.5\times 2256.4

Q_v=1.1282\times 10^{6}\ J

Now the power rating of the boiler:

P=\frac{Q_s+Q_v}{t}

P=\frac{342760+1128200}{1080}

P=1362\ W

Now the time required to heat to boiling point form initial temperature:

t'=\frac{Q_s}{P}

t'=\frac{342760}{1362}

t'=251.659\ s

6 0
3 years ago
Two identical positive charges are placed near each other. At the point halfway between the two chargesTwo identical positive ch
Nitella [24]

Answer:The electric field is zero and the potential is positive.

Explanation:

Two identical positive charges are separated by a certain distance and midway between charges two identical positive charges are placed near each other.

So the Electric field at midway is zero because the electric field due to both charges add up to give zero electric field.(because they point in opposite direction)

Potential is scalar quantity and charges are positive so they add up to give potential.

7 0
2 years ago
A cat walks along a plank with mass M= 6.00 kg. The plank is supported by two sawhorses. The center of mass of the plank is a di
dimulka [17.4K]

Answer:

d₂ = 1.466 m

Explanation:

In this case we must use the rotational equilibrium equations

        Στ = 0

        τ = F r

we must set a reference system, we use with origin at the easel B and an axis parallel to the plank , we will use that the counterclockwise ratio is positive

      + W d₁ - w_cat d₂ = 0

      d₂ = W / w d₁

      d₂ = M /m d₁

      d₂ = 5.00 /2.9    0.850

      d₂ = 1.466 m

6 0
3 years ago
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