A rock of mass 5kg is pushed over the edge of a cliff which is 200m high
1.ignore air resistance and calculate the speed of the rock at the bottom of the cliff. In reality air resistance cannot be ignored. The rock eventually reaches terminal velocity of 30m/s
2.calculate the kinetic energy of the rock at the bottom of the cliff
3.calculate work done by air resistance
4.calculate the average force exerted by air on the rock
ignoring air resistance, vf^2=2gh
2. with a terminal velocity of 30m/s
final KE=1/2 m 30^2
3. work done by fricion= mgh-1/2 m (30^2)
4. average force by air resistance over the entire flight..
avgforce*h= work done by friction
Thanks for number one is the speed 62.61m/s or 2.25m/s???
And on number 5. The force is 37.75 N am I correct?
1. Well, let's start by ignoring air resistance because it's such a drag (pun intended). We can use the good ol' kinematic equations to figure out the speed at the bottom of the cliff. We know the height (200m) and the acceleration due to gravity (approximately 9.8 m/s^2). Plugging those values into the equation for final velocity, we get:
v^2 = u^2 + 2as
where u is the initial velocity (which is zero since it was pushed over the edge) and a is the acceleration due to gravity. So, solving for v:
v^2 = 0^2 + 2(9.8)(200)
v^2 = 0 + 3920
v ≈ √3920
v ≈ 62.57 m/s
So, without air resistance, the speed of the rock at the bottom of the cliff would be approximately 62.57 m/s. Wheee!
2. To calculate the kinetic energy of the rock at the bottom of the cliff, we can use the good old kinetic energy formula, which is:
KE = (1/2)mv^2
where m is the mass of the rock (5 kg) and v is the speed we just calculated (62.57 m/s). Plugging in those values, we get:
KE = (1/2)(5)(62.57)^2
KE = (1/2)(5)(3924.1449)
KE ≈ 19620.7245 J
So, the kinetic energy of the rock at the bottom of the cliff would be approximately 19620.7245 Joules.
3. Since air resistance is not negligible in reality, let's calculate the work done by air resistance. Work is calculated using the formula:
Work = Force x Distance
But since the force of air resistance changes continuously, we can use the formula:
Total Work = integral of F(x) dx
However, we're not given any information about the nature of the air resistance force as a function of distance, so we can't calculate it accurately. Sorry, that's a tough nut to crack!
4. Similarly, calculating the average force exerted by air on the rock is quite challenging without knowing the specific function of air resistance force with respect to time or distance. It's like trying to catch a cloud - you can't grab hold of it easily!
To calculate the speed of the rock at the bottom of the cliff, we can use the principle of conservation of energy. The potential energy of the rock at the top of the cliff is converted into kinetic energy at the bottom. Therefore, we can equate the potential energy to the kinetic energy.
1. Speed of the rock at the bottom of the cliff:
We need to calculate the potential energy of the rock at the top of the cliff first using the formula: Potential Energy (PE) = mass (m) x acceleration due to gravity (g) x height (h)
PE = 5kg x 9.8m/s^2 x 200m = 9800 J (joules)
Since the potential energy at the top is fully converted into kinetic energy at the bottom, we can equate them:
PE = KE
9800 J = (1/2) x mass x velocity^2
Plugging in the known values, we get:
9800 J = 0.5 x 5kg x velocity^2
Simplifying the equation:
velocity^2 = (2 x 9800 J) / 5kg
velocity^2 = 3920 J / 5kg
velocity^2 = 784 m^2/s^2
Taking the square root of both sides:
velocity = √(784 m^2/s^2)
velocity = 28 m/s
Therefore, the speed of the rock at the bottom of the cliff, ignoring air resistance, is 28 m/s.
2. Kinetic energy of the rock at the bottom of the cliff:
The kinetic energy (KE) of an object is given by the formula: KE = (1/2) x mass x velocity^2
Plugging in the known values:
KE = 0.5 x 5kg x (28 m/s)^2
KE = 0.5 x 5kg x 784 m^2/s^2
KE = 1960 J
Therefore, the kinetic energy of the rock at the bottom of the cliff is 1960 Joules.
3. Work done by air resistance:
Since air resistance cannot be ignored, it does work on the falling rock, resulting in a loss of mechanical energy. The work done by air resistance is equal to the change in mechanical energy.
Work = Initial Energy - Final Energy
Work = PE (at the top) - KE (at the bottom)
Work = 9800 J - 1960 J
Work = 7840 J
Therefore, the work done by air resistance is 7840 Joules.
4. Average force exerted by air on the rock:
The average force exerted by air on the rock can be calculated by dividing the work done by air resistance by the distance over which it is applied.
Average force = Work / Distance
The distance in this case is the height of the cliff, which is 200m.
Average force = 7840 J / 200m
Average force = 39.2 N
Therefore, the average force exerted by air on the rock is 39.2 Newtons.