1. We can use the following equation of motion to calculate the speed of the rock at the bottom of the cliff, ignoring air resistance:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity (0 m/s in this case as the rock is initially at rest), a is acceleration due to gravity (approximately 9.81 m/s^2), and s is the displacement (200 m).
v^2 = 0 + 2 * 9.81 * 200
v^2 = 3924
v = sqrt(3924) = 62.6 m/s (approximately)
2. Now we can calculate the kinetic energy of the rock at the bottom of the cliff. Kinetic energy is given by the equation:
KE = 1/2 * m * v^2
where m is the mass of the rock (5 kg) and v is its final velocity (62.6 m/s, approximately).
KE = 1/2 * 5 * (62.6)^2 = 0.5 * 5 * 3918.76 = 9789.4 J (approximately)
3. Since we know that the rock eventually reaches a terminal velocity of 30 m/s, we can calculate the kinetic energy at this point using the same equation.
KE_terminal = 1/2 * m * v_terminal^2
KE_terminal = 1/2 * 5 * (30)^2 = 0.5 * 5 * 900 = 2250 J
Now we can find the work done by air resistance by finding the difference between the kinetic energy without air resistance and the kinetic energy at terminal velocity.
Work_air = KE - KE_terminal = 9789.4 - 2250 = 7539.4 J (approximately)
4. To calculate the average force exerted by air on the rock, we can use the work-energy principle:
Work = Force x distance
In this case, the distance is the height of the cliff, which is 200 m. We can rearrange the equation to solve for the force:
Force = Work / distance = 7539.4 / 200 = 37.7 N (approximately)
So the average force exerted by air on the rock is 37.7 N.
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
1 answer