Please correctly match each term.
A 3-kg object is dropped from a height of 5 m. The rock has an impact speed of...
A ball is rolled up a hill and comes to rest at a height of 10 m. Its original speed was about...
A ball is rolled up a hill with an initial speed of 3 m/s. To what height would it reach before coming to a stop.
A roller coaster needs to climb a tall hill. How tall of a hill can it climb with an initial sped of 15 m.s.
A child on a swing falls a height of 1m. What speed will the child reach?
A 1-kg toy car flies of a 1-m tall table at 2 m/s. Approximately what energy does it have when it strikes the floor?
12 joules
10 m/s
11.25 m
14.1 m/s
4.5 m/s
6.7 m
These questions are all the same.
If there is no loss of energy of the system to heat or elsewhere the sum of potential and kinetic energy is constant
(1/2) m v^2 + m g h = constant
so for example
(1/2) m 0 ^2 + m (9.81) * 5= (1/2) m v^2 + m (9.81) * 0
or
(1/2)v^2 =9.81 * 5 [ note m does not matter if no change in mass]
v = sqrt (98.1) = 9.90 m/s
note if you used g = 10 the answer would be 10
by the way most of us try to remember that v= sqrt (2 g h)
To match each term correctly, we need to use the equations of motion related to free fall and kinetic energy. Let's go through each question one by one:
1. A 3-kg object is dropped from a height of 5 m. The rock has an impact speed of...
To find the impact speed, we can use the equation of motion for free fall:
v^2 = u^2 + 2as
In this case, the initial velocity (u) is 0 (since the object is being dropped) and the acceleration (a) is due to gravity, which is approximately 9.8 m/s^2. The displacement (s) is -5 m (negative because it is downward). Plugging these values into the equation, we get:
v^2 = 0^2 + 2 * 9.8 * -5
v^2 = -98
v ≈ √(-98) [taking the square root of both sides]
v ≈ 9.9 m/s
Therefore, the impact speed of the 3-kg object is approximately 9.9 m/s.
2. A ball is rolled up a hill and comes to rest at a height of 10 m. Its original speed was about...
To find the original speed, we can use the conservation of energy principle. The potential energy at the top of the hill is equal to the initial kinetic energy. The potential energy is given by:
PE = mgh
where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
The initial kinetic energy can be calculated using the equation:
KE = 1/2 * m * v^2
where v is the initial velocity.
Taking the potential energy equal to the initial kinetic energy, we have:
mgh = 1/2 * m * v^2
Canceling out the mass and rearranging the equation, we get:
v^2 = 2gh
v = √(2gh)
Plugging in the values, we have:
v = √(2 * 9.8 * 10)
v ≈ √196
v ≈ 14 m/s
Therefore, the original speed of the ball was approximately 14 m/s.
3. A ball is rolled up a hill with an initial speed of 3 m/s. To what height would it reach before coming to a stop.
To find the height the ball reaches, we can once again use the conservation of energy principle. At the top of the hill, the kinetic energy is zero, so all the initial kinetic energy is converted into potential energy.
Using the same equation as before:
KE = 1/2 * m * v^2
PE = mgh
Since the ball comes to a stop, the final kinetic energy is zero. Therefore, we have:
1/2 * m * (0^2) = mgh
0 = mgh
h = 0
This means that the ball would not reach any height since it comes to a stop before reaching the top of the hill.
4. A roller coaster needs to climb a tall hill. How tall of a hill can it climb with an initial speed of 15 m/s?
To find the maximum height the roller coaster can climb, we can again use the conservation of energy principle. At the highest point, all the initial kinetic energy should be converted into potential energy.
Using the same equations as before, we have:
KE = 1/2 * m * v^2
PE = mgh
Setting the final kinetic energy equal to zero, we have:
1/2 * m * (0^2) = mgh
0 = mgh
h = 0
This means that the roller coaster can theoretically reach an infinite height since there is no restriction based on its initial speed. So, it can climb any height of the hill.
5. A child on a swing falls a height of 1m. What speed will the child reach?
To find the speed the child will reach when falling, we can use the equation of motion for free fall again. The initial velocity is zero since the child is initially at rest.
Using the equation:
v^2 = u^2 + 2as
Where u is the initial velocity, a is the acceleration due to gravity (approximately 9.8 m/s^2), and s is the distance fallen.This time, we have:
v^2 = 0^2 + 2 * 9.8 * 1
v^2 = 19.6
v ≈ √19.6
v ≈ 4.4 m/s
Therefore, the child will reach a speed of approximately 4.4 m/s when falling.
6. A 1-kg toy car flies off a 1-m tall table at 2 m/s. Approximately what energy does it have when it strikes the floor?
To find the energy the toy car has when it strikes the floor, we need to consider both its kinetic energy and potential energy at that point.
The kinetic energy is given by the equation:
KE = 1/2 * m * v^2
The potential energy is given by the equation:
PE = mgh
Since the toy car is flying off the table, its height (h) when it strikes the floor is zero.
So, the total energy at that point is the sum of kinetic and potential energy:
Total energy = KE + PE
Using the given values, we have:
KE = 1/2 * 1 * 2^2
KE = 1 * 4/2
KE = 2 J
PE = 1 * 9.8 * 1
PE = 9.8 J
Total energy = 2 J + 9.8 J
Total energy = 11.8 J
Therefore, the toy car has approximately 11.8 joules of energy when it strikes the floor.