A 0.18-kg ball on a stick is whirled on a vertical circle at a constant speed. When the ball is at the three o’clock position, t
1 answer:
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The given from your problem are the following:
V = 85mph (This is miles per hour)
d = 60 feet
If you notice the units do not match. Before we can do anything else, we need to make the figures match.
In this case, we will convert 85miles per hour to feet per hour. There are 5,280 feet in 1 mile.
x 
But wait! If you think about the scenario, you are looking for how long it will take for the ball to reach the bat. The most applicable unit of time to use here is second. It would be very hard to really measure a short and instantaneous event in hours. So we convert it into feet per second:
There are 3,600 seconds in 1 hour.
x 
So now we have our new given as:
v = 124.67ft/s
d = 60 ft
The formula for time can be derived from the formula from velocity, which is:
The formula of time will then be:
All you need to do is plug in what you know and solve for what you don't know.
The answer then is 0.48s.
If you want this in hours, just divide the value in seconds by 3,600. The answer would then be 0.00013hr. (See how small it is? This is why seconds would be a more appropriate measure.)
V = 85mph (This is miles per hour)
d = 60 feet
If you notice the units do not match. Before we can do anything else, we need to make the figures match.
In this case, we will convert 85miles per hour to feet per hour. There are 5,280 feet in 1 mile.
But wait! If you think about the scenario, you are looking for how long it will take for the ball to reach the bat. The most applicable unit of time to use here is second. It would be very hard to really measure a short and instantaneous event in hours. So we convert it into feet per second:
There are 3,600 seconds in 1 hour.
So now we have our new given as:
v = 124.67ft/s
d = 60 ft
The formula for time can be derived from the formula from velocity, which is:
The formula of time will then be:
All you need to do is plug in what you know and solve for what you don't know.
The answer then is 0.48s.
If you want this in hours, just divide the value in seconds by 3,600. The answer would then be 0.00013hr. (See how small it is? This is why seconds would be a more appropriate measure.)
Answer:
(a) the final velocity of the cart is 0.857 m/s
(b) the impulse experienced by the package is 21.43 kg.m/s
(c) the fraction of the initial energy lost is 0.71
Explanation:
Given;
mass of the package, m₁ = 10 kg
mass of the cart, m₂ = 25 kg
initial velocity of the package, u₁ = 3 m/s
initial velocity of the cart, u₂ = 0
let the final velocity of the cart = v
(a) Apply the principle of conservation of linear momentum to determine common final velocity for ineleastic collision;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
10 x 3 + 25 x 0 = v(10 + 25)
30 = 35v
v = 30 / 35
v = 0.857 m/s
(b) the impulse experienced by the package;
The impulse = change in momentum of the package
J = ΔP = m₁v - m₁u₁
J = m₁(v - u₁)
J = 10(0.857 - 3)
J = -21.43 kg.m/s
the magnitude of the impulse experienced by the package = 21.43 kg.m/s
(c)
the initial kinetic energy of the package is calculated as;
the final kinetic energy of the package;
the fraction of the initial energy lost;