Answer:
The velocity of the center of mass of the two-ball system is 13.1 m/s.
Explanation:
Given;
mass of the first ball, m₁ = 0.5 kg
mass of the second ball, m₂ = 0.25 kg
initial velocity of the second ball, u₂ = 19.6 m/s
At the highest point the velocity of the second ball, v₂ = 0
The highest point reached by the second ball is calculated as;
v₂² = u₂² - 2gh
0 = u₂² - 2gh
2gh = u₂²
h = u₂² / 2g
h = (19.6²) / (2 x 9.8)
h = 19.6 m
The final velocity of the first ball when it had traveled 19.6 m down;
v₁² = u₁² + 2gh
v₁² = 0 + 2gh
v₁ = √2gh
v₁ = √(2 x 9.8 x 19.6)
v₁ = 19.6 m/s
The velocity of the center of mass of the two-ball system is calculated as;
Answer:
Final Length = 30 cm
Explanation:
The relationship between the force applied on a string and its stretching length, within the elastic limit, is given by Hooke's Law:
F = kΔx
where,
F = Force applied
k = spring constant
Δx = change in length of spring
First, we find the spring constant of the spring. For this purpose, we have the following data:
F = 50 N
Δx = change in length = 25 cm - 20 cm = 5 cm = 0.05 m
Therefore,
50 N = k(0.05 m)
k = 50 N/0.05 m
k = 1000 N/m
Now, we find the change in its length for F = 100 N:
100 N = (1000 N/m)Δx
Δx = (100 N)/(1000 N/m)
Δx = 0.1 m = 10 cm
but,
Δx = Final Length - Initial Length
10 cm = Final Length - 20 cm
Final Length = 10 cm + 20 cm
<u>Final Length = 30 cm</u>
Answer:
26.5m/s²
Explanation:
Given parameters:
Tangential velocity of the object = 23m/s
Radius of track = 20m
Unknown:
Acceleration = ?
Solution:
The acceleration of the body is its centripetal acceleration. It is given by;
a =
v is the tangential velocity
r is the
a = = 26.5m/s²
Answer:
y = 0m
y0 = 166m
v0y = 0 m/s
g = 9.8 m/s^2
t = ?
Solve for t:
y = y0 + v0y*t - (0.5)gt^2
0 = 166 - (0.5)(9.8)t^2
t = 5.82 s
Now, using time, we can solve for the range using the equation:
x = vx(t)
x = (40)(5.82)
x = 232.8 m
The impact horizontal component of velocity will be 40 m/s as velocity in terms of x is always constant. To find the impact vertical component of velocity, we use the equation:
v = v0y - gt
v = 0 - (9.8)(5.82)
v = -57.04 m/s
Explanation:
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