The graph shows a ball rolling from A to G. At which point does the ball have the greatest kinetic energy?
2 answers:
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Answer:
F = 63N
Explanation:
M= 1.5kg , t= 2s, r = (2t + 10)m and
Θ = (1.5t² - 6t).
magnitude of the resultant force acting on 1.5kg = ?
Force acting on the mass =
∑Fr =MAr
Fr = m(∇r² - rθ²) ..........equation (i)
∑Fθ = MAθ = M(d²θ/dr + 2dθ/dr) ......... equation (ii)
The horizontal path is defined as
r = (2t + 10)
dr/dt = 2, d²r/dt² = 0
Angle Θ is defined by
θ = (1.5t² - 6t)
dθ/dt = 3t, d²θ/dt² = 3
at t = 2
r = (2t + 10) = (2*(2) +10) = 14
but dr/dt = 2m/s and d²r/dt² = 0m/s
θ = (1.5(2)² - 6(2) ) = -6rads
dθ/dt =3(2) - 6 = 0rads
d²θ/dt = 3rad/s²
substituting equation i into equation ii,
Fr = M(d²r/dt² + rdθ/dt) = 1.5 (0-0)
∑F = m[rd²θ/dt² + 2dr/dt * dθ/dt]
∑F = 1.5(14*3+0) = 63N
F = √(Fr² +FΘ²) = √(0² + 63²) = 63N
The ball raised up the hill is given gravitational potential energy, which
causes it to roll spontaneously down the hill.
The statement that explains whether the ball rolling down the hill
experiment should be used is; <u>The experiment shows the ball falls toward </u>
<u>the bottom of the hill, so it provides direct evidence that gravity pulls an </u>
<u>object downward. They should use it.</u>
Reason:
The equation for the velocity of a ball falling down a hill is
Therefore, by increasing the height from which the ball rolls down the hill,
the velocity of the ball increases, which indicates that the ball is
accelerating, and therefore, being acted on by a force, the force of gravity.
Therefore;
Given that the ball falls or moves with increasing speed towards
the bottom of the hill, which shows that the motion is due to Earth's pull
known as the gravitational force, the experiment should be used.
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