A ball is rolled along the inside of a partial hoop lying flat on a table. which path will the ball follow when it gets to the e
nd of the hoop?
2 answers:
Explanation :
A ball is rolled along the inside of a partial hoop lying flat on a table. The ball will move in a straight path as shown in the attached figure.
The figure shows a semicircular hoop. When the ball reaches at the other end, it will move tangentially.
In a circular path, the object move with constant speed but the velocity changes at every instant.
So, the ball will move in a straight line when it reaches at the end of the hoop.
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Answer:
The tension in each half of the rope, is approximately 4,908.8 N
Explanation:
The mass of the acrobat, m = 60 kg
The length of the rope, l = 10 m
The extent by which the center dropped = 30 cm = 0.3 m
Let, 'T' represent the tension in each half of the rope
Weight, W = Mass, m × The acceleration due to gravity, g
∴ W = m × g
The acceleration due to gravity, g ≈ 9.8 m/s²
∴ The weight of the acrobat, W = 60 kg × 9.8 m/s² ≈ 588 N
The angle the dropped rope makes with the horizontal, θ is given as follows;
θ = arctan((0.3 m)/(5 m)) = arctan(0.06) ≈ 3.434°
At equilibrium, the sum of vertical forces, = 0
The vertical component of the tension, , in each half of the rope is given as follows;
= T × sin(θ)
∴ = W + T × sin(θ) + T × sin(θ) = W + 2 × T × sin(θ)
Plugging in the values, with θ = arctan(0.06) for accuracy, we get;
588 N + 2 × T × sin(arctan(0.06) = 0
∴ 2 × -T × sin(arctan(0.06) = 588 N
-T= 588 N/(2 × sin(arctan(0.06)) = 4,908.81208 N ≈ 4,908.8 N
The tension in each half of the rope, T ≈ 4,908.8 N.
Answer:
Distance covered by B is 4 times distance covered by A
Explanation:
For an object in free fall starting from rest, the distance covered by the object in a time t is
where
s is the distance covered
g is the acceleration due to gravity
t is the time elapsed
In this problem:
- Object A falls through a distance during a time t, so the distance covered by object A is
- Object B falls through a distance during a time 2t, so the distance covered by object B is
So, the distance covered by object B is 4 times the distance covered by object A.