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Neporo4naja [7]
3 years ago
11

A block of mass m slides with a speed vo on a frictionless surface and collides with another mass M which is initially at rest.

The two blocks stick together and move with a speed of vo /3. In terms of m, mass M is most nearly_____.
Physics
1 answer:
Rudik [331]3 years ago
3 0

To solve this problem we will apply the concepts related to the conservation of momentum. Momentum can be defined as the product between mass and velocity. We will depart to facilitate the understanding of the demonstration, considering the initial and final momentum separately, but for conservation, they will be later matched. Thus we will obtain the value of the mass. Our values will be defined as

m_1 = m

m_2 = M

v_{1i} =v_0

v_{2i} = 0

Initial momentum will be

P_i = m_iv_{1i}+m_2v_{2i}

P_i = mv_0

After collision

v_{1f} = v_{2f} = \frac{v_0}{3}

Final momentum

P_f = (m_1+m_2)(\frac{v_0}{3})

P_f = (m+M)(\frac{v_0}{3})

From conservation of momentum

P_f = P_i

Replacing,

(m+M)(\frac{v_0}{3})=mv_0

(m+M)\frac{1}{3} = m

m+M=3m

M=3m-m

M=2m

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Answer:

a) The mass flow rate through the nozzle is 0.27 kg/s.

b) The exit area of the nozzle is 23.6 cm².

Explanation:

a) The mass flow rate through the nozzle can be calculated with the following equation:

\dot{m_{i}} = \rho_{i} v_{i}A_{i}

Where:

v_{i}: is the initial velocity = 20 m/s

A_{i}: is the inlet area of the nozzle = 60 cm²  

\rho_{i}: is the density of entrance = 2.21 kg/m³

\dot{m} = \rho_{i} v_{i}A_{i} = 2.21 \frac{kg}{m^{3}}*20 \frac{m}{s}*60 cm^{2}*\frac{1 m^{2}}{(100 cm)^{2}} = 0.27 kg/s  

Hence, the mass flow rate through the nozzle is 0.27 kg/s.

b) The exit area of the nozzle can be found with the Continuity equation:

\rho_{i} v_{i}A_{i} = \rho_{f} v_{f}A_{f}

0.27 kg/s = 0.762 kg/m^{3}*150 m/s*A_{f}

A_{f} = \frac{0.27 kg/s}{0.762 kg/m^{3}*150 m/s} = 0.00236 m^{2}*\frac{(100 cm)^{2}}{1 m^{2}} = 23.6 cm^{2}

Therefore, the exit area of the nozzle is 23.6 cm².

I hope it helps you!                                                                  

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