Answer:
15.4 kg.
Explanation:
From the law of conservation of momentum,
Total momentum before collision = Total momentum after collision
mu+m'u' = V(m+m').................... Equation 1
Where m = mass of the first sphere, m' = mass of the second sphere, u = initial velocity of the first sphere, u' = initial velocity of the second sphere, V = common velocity of both sphere.
Given: m = 7.7 kg, u' = 0 m/s (at rest)
Let: u = x m/s, and V = 1/3x m/s
Substitute into equation 1
7.7(x)+m'(0) = 1/3x(7.7+m')
7.7x = 1/3x(7.7+m')
7.7 = 1/3(7.7+m')
23.1 = 7.7+m'
m' = 23.1-7.7
m' = 15.4 kg.
Hence the mass of the second sphere = 15.4 kg
Answer:
b, the fastest the car has traveled out of those options is 4-5 seconds.
Explanation:
26.10 N is the vertical component of the force.
Rx represents the Horizontal component of force
Ry represents The Vertical component of force
According to the given diagram
Rx - Tcosθ = 0
Rx = Tcosθ
And,
Ry + Tsinθ = mg
Ry = mg - Tsinθ
The horizontal component of force =The Vertical component of force
Rx = Ry
Tcosθ = mg - Tsinθ
T(cosθ + sinθ) = 29 × 9.8 = 284.2 N
T√2 cosθ = 284.2 N
T × √2 ×0.544 = 284.2 N
T × 0.769 = 284.2 N
T = 370 N (app)
So,
Ry = 284.2 - 370 (sin 57°)
= 284.2 - 310.3 = -26.10 N
Hence, 26.10 N is the vertical component of the force exerted.
Learn more about the horizontal and vertical components here
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Answer:
Explanation:
Mass: M, Length: L.
The formula that gives center of mass is
In the case of a non-uniform mass density, this formula converts to
where the denominator is the total mass and the nominator is the mass times position of each point on the rod.
We have to integrate the mass density over the total rod in order to find the total mass. Likewise, we have to integrate the center of mass of each point (xσ(x)) over the total rod. And if we divide the integrated center of mass to the total mass, we find the center of mass of the rod:
Here x's are cancelled. Otherwise, the denominator would be zero.
Power is defined as the amount of work over a certain amount of time. Work is also Force times the distance traveled. Simplifying the expression makes it Power=Force x Velocity. Since we are given that the power is 4500 W and the force is 100 N, dividing the Power by force gives 45 m/s, which is the velocity of the ball.
