How high will a 1.85 kg rock go if thrown straight up by someone who expends 80.0 J of energy on it?
Kinetic energy at ground = 80
Kinetic energy at max height = 0
so
Potential energy at max height = 80
so
m g h = 80
h = 80/(1.85*9.81)
Kinetic energy at ground = 80
Kinetic energy at max height = 0
so
Potential energy at max height = 80
so
m g h = 80
h = 80/(1.85*9.81)
Well, let's do some calculations here. If the rock is thrown straight up, it will experience a gravitational force pulling it back down. Now, assuming the rock doesn't have any special powers like anti-gravity, it will eventually come back down to Earth.
But let's find out how high it goes first! We know that the person expends 80.0 J of energy on the rock, so we can use that to find the rock's final velocity using the equation
kinetic energy = (1/2) * mass * velocity^2
Since the initial velocity is zero (I mean, you can't throw a rock that's already moving, right?), the rock's kinetic energy will be equal to the energy expended on it. Therefore, we have
80.0 J = (1/2) * 1.85 kg * velocity^2
Now, solving for velocity, we get
velocity^2 = (80.0 J * 2) / 1.85 kg
velocity^2 = 86.486 J/kg
velocity ≈ 9.3 m/s
Alright, now comes the fun part. We can use the equation
velocity^2 = initial velocity^2 + 2 * gravity * height
Since we're looking for the maximum height (when the rock momentarily stops moving), we know the final velocity is zero. So we can rewrite the equation as
0 = 9.3 m/s^2 - 2 * 9.8 m/s^2 * height
Simplifying,
0 = 9.3 m/s^2 - 19.6 m/s^2 * height
Now, solving for height, we find
height = 9.3 m/s^2 / 19.6 m/s^2
height ≈ 0.474 m
So, the rock will go up approximately 0.474 meters high! Though, it might not be impressed by its height. But hey, at least it got to experience a few moments of weightlessness, right?
To determine how high the rock will go when thrown straight up, we can use the principle of conservation of energy. The initial energy expended on the rock is equal to the potential energy when it reaches its highest point. Here are the steps to calculate the height:
1. Find the potential energy (PE) using the formula: PE = m * g * h, where m is the mass of the rock (1.85 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height.
2. Rearrange the formula to solve for h:
PE = m * g * h
h = PE / (m * g)
3. Substitute the values into the equation:
h = 80.0 J / (1.85 kg * 9.8 m/s²)
4. Calculate the height:
h ≈ 4.53 meters
Therefore, the rock will go approximately 4.53 meters high when thrown straight up by someone who expends 80.0 J of energy on it.
To determine how high the rock will go when thrown straight up, we need to consider principles of energy conservation. The potential energy gained by the rock will be equal to the work done on it.
First, we calculate the potential energy gained by the rock. The potential energy (PE) is given by the formula:
PE = m * g * h
Where:
m = mass of the rock (1.85 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height attained by the rock (unknown)
Next, we calculate the work done (W) on the rock, which is equal to the energy expended on it:
W = 80.0 J
Since the work done on the rock is equal to the potential energy gained, we equate these two equations:
W = PE
80.0 J = m * g * h
Rearranging the equation, we solve for h:
h = (W) / (m * g)
h = 80.0 J / (1.85 kg * 9.8 m/s^2)
Evaluating the expression, we find:
h ≈ 4.31 meters
Therefore, the rock will go approximately 4.31 meters high when thrown straight up by someone who expends 80.0 J of energy on it.