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Temka [501]
3 years ago
10

A felt-covered beanbag is fired into a empty wooden crate that sits on a concrete floor and is open on one side. The beanba

g is moving exactly horizontally when it strikes and sticks to the inside wall of the crate, which is lined with velcro. As a result of this impact, the crate slides backwards 0.935 meters along the concrete, which has a coefficient of kinetic friction of \mu_k = 0.480μ ​k ​​ =0.480. The beanbag has a mass of 0.354 kg and the empty crate has a mass of 3.77 kg. Calculate the speed of the beanbag vv at the moment it strikes the crate. You may neglect the effect of air resistance.
Physics
1 answer:
Phantasy [73]3 years ago
8 0

Answer:

31.42383 m/s

Explanation:

g = Acceleration due to gravity = 9.81 m/s²

\mu = Coefficient of kinetic friction = 0.48

s = Displacement = 0.935 m

m_1 = Mass of bean bag = 0.354 kg

m_2 = Mass of empty crate = 3.77 kg

v_1 = Speed of the bean bag

v_2 = Speed of the crate

Acceleration

a=-\frac{f}{m}\\\Rightarrow a=-\frac{\mu mg}{m}\\\Rightarrow a=-\mu g

a=--9.81\times 0.48=4.7088\ m/s^2

From equation of motion

v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 4.7088\times 0.935+0^2}\\\Rightarrow v=2.96739\ m/s

In this system the momentum is conserved

m_1v_1=(m_1+m_2)v_2\\\Rightarrow v_1=\frac{(m_1+m_2)v_2}{m_1}\\\Rightarrow u=\frac{(0.354+3.77)\times 2.69739}{0.354}\\\Rightarrow u=31.42383\ m/s

The speed of the bean bag is 31.42383 m/s

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