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Scilla [17]
3 years ago
15

The 25 kg wheel has a radius of gyration about its center O of kO = 300 mm. When the wheel is subjected to the couple moment, it

slips as it rolls. Determine the angular acceleration of the wheel and the acceleration of the wheel's center O. The coefficient of kinetic friction between the wheel and the plane is μk = 0.6.
Physics
1 answer:
N76 [4]3 years ago
3 0

Answer:

Explanation:

radius of gyration of wheel k then

k² = r²/2

r² = 2 k²

r = √2 k

= 1.414 x .3 m

r = .4242 m

Moment of inertia of wheel

= mass x radius of gyration ²

= 25 x .3 x .3

= 2.25 kg m²

Friction force acting on it ( sliding )

= μmg , μ being coefficient of kinetic friction

This friction force will create linear acceleration in forward direction

Acceleration produced

= μg

= .6 x 9.8

= 5.88 m / s ²

This will also rotate the wheel , angular acceleration being

linear acceleration / radius

= 5.88 /.4242

= 13.86 radian / s²

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a mass of 1.00 kg of water at temperature T is poured from a height of 0.100 km into a vessel containing water of the same tempe
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m_wgh=m_wc\Delta T+m_vc\Delta T\\\Rightarrow m_v=\dfrac{m_wgh-m_wc\Delta T}{c\Delta T}\\\Rightarrow m_v=\dfrac{m_wgh}{c\Delta T}-m_w\\\Rightarrow m_v=\dfrac{1\times 9.81\times 100}{4186\times 0.1}-1\\\Rightarrow m_v=1.34352\ kg

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6 0
3 years ago
15. If an 800.-kg sports car slows to 13.0 m/s to check out an accident scene and the
goldfiish [28.3K]

The final combined velocity after the collision is 20.2 m/s

Explanation:

We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two car and of the truck must be conserved before and after the collision.

This means that we can write the following equation:

p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v  

where:  

m_1 = 800 kg is the mass of the sport car

u_1 = 13.0 m/s is the initial velocity of the car (taking its direction as positive  direction)

m_2 = 1200 kg is the mass of the truck

u_2 = 25.0 m/s is the initial velocity of the truck

v is the final combined velocity of the car and the truck, after the collision

Re-arranging the equation and substituting the values, we find the velocity after the collision:

v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(800)(13)+(1200)(25)}{800+1200}=20.2 m/s

And the positive sign indicates their final direction is the same as the initial direction of the two vehicles.

Learn more about momentum here:

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