You are on roller blades on top of a small hill. Your potential energy is equal to 1,000.0 joules. The last time
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Answer:
i) The period of the particle is 0.3 seconds
ii) The angular velocity is approximately 20.94 rad/s
iii) The linear velocity is approximately 1.047 m/s
iv) The centripetal acceleration is approximately 6.98 m/s²
Explanation:
The given parameters are;
The number of revolution of the particle, n = 800 revolution
The time it takes the particle to make 800 revolutions = 4 minutes
The dimension of the circle = 5 cm = 0.05 m
Given that the dimension of the circle is the radius of the circle, we have;
i) The period of the particle, T = The time to complete one revolution
T = 1/(The number of revolutions per second)
∴ T = 1/(800 rev/(4 min × 60 s/min)) = 3/10 s
The period, T = 3/10 seconds = 0.3 seconds
ii) The angular velocity, ω = Angle covered/(Time)
800 revolutions in 4 minutes = Angle of (800 × 2·π) in 4 minutes
∴ ω = (800 × 2·π)/(4 × 60) = 20·π/3
The angular velocity, ω = 20·π/3 rad/s ≈ 20.94 rad/s
iii) The linear velocity, v = r × ω
∴ The linear velocity, v = 0.05 m × 20·π/3 rad/s = π/3 m/s ≈ 1.047 m/s
iv) The centripetal acceleration, = v²/r
∴ The centripetal acceleration, = (π/3)²/(0.05) = 20·π/9
The centripetal acceleration, = 20·π/9 m/s² ≈ 6.98 m/s²
<h3><u>Full Question:</u></h3>
A 2-kg toy car accelerates from 5 to 10 m/s in 2 seconds. Find the applied force.
<h2><u>Answer:</u></h2>Force applied is .
Force is defined as something which changes or tends to change the velocity of a body. And acceleration is defined as the rate of change of velocity of a body per time. Both of them are vector quantities.
The initial velocity of the body = 5 m/s.
The final velocity of the body = 10 m/s.
So the change in velocity = 10 - 5 m/s = 5m/s.
Time period = 2 seconds.
So acceleration ==
The force is defined as the product of mass and acceleration of the body.
Mass of body = 2 kg.
So, force applied = . =
.