Pls help me solve this question pls. A stone of mass 6.5kg is thrown vertically upward with velocity with 10m/s find a. the potential energy at the greatest height and the value of h .b the kinetic energy of reaching the ground again(g=10m/s2) in physics?
as the stone travels upward, its kinetic energy becomes potential energy
the potential at the top is equal to the kinetic at the bottom
... e = 1/2 m v^2 = m g h
... h = √[v^2 / (2 g)]
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To solve this question, let's break it down step by step:
Step 1: Find the potential energy at the greatest height (h). We can use the formula for potential energy:
Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)
Given:
Mass (m) = 6.5 kg
Gravitational acceleration (g) = 10 m/s^2
Since the stone is thrown vertically upward, it will reach its greatest height when its velocity becomes zero.
To find the height, we need to first find the time it takes for the stone to reach its highest point, using the equation: v = u + gt, where:
- v is the final velocity, which is 0 m/s (at the highest point)
- u is the initial velocity, which is 10 m/s (given)
- g is the gravitational acceleration, which is 10 m/s^2 (given)
- t is the time taken
Rearranging the equation, we have: t = (v - u) / g
Substituting the values, we get: t = (0 - 10) / 10 = -10 / 10 = -1 s
Since time cannot be negative, we take the absolute value of -1, which gives us: t = 1 s
Using this time, we can calculate the height (h) using the equation: h = ut + (1/2)gt^2
Substituting the values, we get: h = (10 * 1) + (1/2)(10)(1^2) = 10 + (1/2)(10)(1) = 10 + 5 = 15 m
So, the height (h) at the greatest point is 15 meters.
Step 2: Find the kinetic energy of the stone when it reaches the ground.
We know that the potential energy at the highest point will be completely converted to kinetic energy when the stone falls back down to the ground.
Since the potential energy at the greatest height is equal to the kinetic energy when it reaches the ground, we can use the same formula:
Potential Energy (PE) = Kinetic Energy (KE)
Using the formula for potential energy: PE = mass (m) * gravitational acceleration (g) * height (h)
Substituting the values, we get: PE = 6.5 kg * 10 m/s^2 * 15 m = 975 J (Joules)
Therefore, the kinetic energy of the stone when it reaches the ground is 975 Joules.
To solve this question, we'll break it down into two parts - finding the potential energy at the greatest height and finding the kinetic energy when it reaches the ground again.
a. Potential Energy at the Greatest Height:
The potential energy of an object is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
Mass of the stone (m) = 6.5 kg
Vertical velocity of the stone (u) = 10 m/s
Acceleration due to gravity (g) = 10 m/s^2 (assuming standard Earth gravity)
To find the potential energy (PE), we need to determine the height (h) at the greatest point the stone reaches. The vertical velocity at the highest point will be zero, as it momentarily comes to rest before falling back down.
Using the equation v^2 = u^2 + 2gh, where v is the final velocity (which is zero at the highest point), we can solve for h:
0^2 = 10^2 + 2(10)(h)
0 = 100 + 20h
20h = -100
h = -100/20
h = -5 meters
The height (h) in this case is negative because it represents the displacement in the opposite direction (downwards) from the stone's initial position.
Now, substituting the values in the potential energy formula, we have:
PE = mgh
PE = 6.5 kg * 10 m/s^2 * (-5 m)
PE = -325 Joules
Therefore, the potential energy at the greatest height is -325 Joules.
b. Kinetic Energy when Reaching the Ground Again:
To find the kinetic energy when the stone reaches the ground, we can use the formula KE = 1/2 * mv^2, where m is the mass and v is the velocity.
Given:
Mass of the stone (m) = 6.5 kg
Acceleration due to gravity (g) = 10 m/s^2
To find the velocity (v) when the stone reaches the ground, we can use the formula v = u + gt, where u is the initial velocity and t is the time taken.
The stone was thrown vertically upward, so the initial velocity (u) is 10 m/s.
At the highest point, the velocity becomes zero, and the stone will take the same amount of time to fall back to the ground.
So, the time taken to reach the ground (t) is equal to the time it took to reach the highest point.
Using the equation v = u + gt, we can solve for t:
0 = 10 + 10t
10t = -10
t = -10/10
t = -1 second
Again, the time is negative because it represents the time taken in the opposite direction.
Now, we can find the final velocity:
v = u + gt
v = 10 + 10(-1)
v = 10 - 10
v = 0 m/s
Substituting values in the kinetic energy formula, we have:
KE = 1/2 * mv^2
KE = 1/2 * 6.5 kg * (0 m/s)^2
KE = 0 Joules
Therefore, the kinetic energy when the stone reaches the ground again is 0 Joules.
In summary:
a. The potential energy at the greatest height is -325 Joules, and the value of h is -5 meters.
b. The kinetic energy when reaching the ground again is 0 Joules.