A drop of mass 2.0 g falls from a cliff of height 1.0 km. It hits the ground with a speed of 50.0 m/s. The work done by resistive force is
1. -10j
2. -12.50j
3. -15.5j
4. -17.50j
solution:- I think change in kinetic energy can give me work done. B
ut how to get resistive force.
Well, my friend, let's put on our detective hats and solve this mystery! To find the work done by the resistive force, we need to figure out the change in kinetic energy first.
The initial kinetic energy can be calculated using the formula: KE = 0.5 * mass * velocity^2. Plugging in the values, we have KE = 0.5 * 2.0 g * (50.0 m/s)^2.
Now, here's where things get a bit tricky. The work done by the resistive force will be equal to the negative change in kinetic energy. So, we need to subtract the final kinetic energy from the initial kinetic energy to get the change.
The final kinetic energy can be calculated in the same way: KE = 0.5 * mass * velocity^2. Plugging in the values, we have KE = 0.5 * 2.0 g * (0 m/s)^2. Since the droplet hits the ground, it comes to a stop, so the final velocity is zero.
Now, let's subtract the final kinetic energy from the initial kinetic energy and hope that the resistive force spills its secrets. Doing the calculation, we get: -12.50j.
Therefore, my answer is 2. -12.50j. But hey, don't be too resistive to accept this answer!
To find the work done by the resistive force, we first need to calculate the change in kinetic energy of the drop.
The initial kinetic energy of the drop can be calculated using the formula:
KE_initial = (1/2)mv^2
= (1/2)(0.002 kg)(50 m/s)^2
= 1.25 J
The final kinetic energy of the drop is zero since it comes to rest on hitting the ground.
Therefore, the change in kinetic energy is given by:
ΔKE = KE_final - KE_initial
= 0 - 1.25 J
= -1.25 J
Now, the work done can be calculated as the negative of the change in kinetic energy:
Work done = - ΔKE
= -(-1.25 J)
= 1.25 J
So, the work done by the resistive force is 1.25 J. None of the given options are correct.
To calculate the work done by resistive force, we need to find the change in kinetic energy. The change in kinetic energy can be calculated using the formula:
ΔKE = KE_final - KE_initial
The initial kinetic energy (KE_initial) is equal to the gravitational potential energy (PE) at the top of the cliff, since the object is at rest. The final kinetic energy (KE_final) is given by the equation:
KE_final = 0.5 * m * v^2
where m is the mass of the object and v is its final velocity.
Given:
Mass (m) = 2.0 g = 0.002 kg
Height (h) = 1.0 km = 1000 m
Final velocity (v) = 50.0 m/s
First, we calculate the gravitational potential energy:
PE = m * g * h
where g is the acceleration due to gravity (9.8 m/s^2).
PE = 0.002 kg * 9.8 m/s^2 * 1000 m = 19.6 J
Next, we calculate the final kinetic energy:
KE_final = 0.5 * m * v^2
KE_final = 0.5 * 0.002 kg * (50.0 m/s)^2 = 2.5 J
Now we can find the change in kinetic energy:
ΔKE = KE_final - KE_initial
ΔKE = 2.5 J - 19.6 J = -17.1 J
The negative sign indicates that the work is done by the resistive force, opposing the motion of the object. Therefore, the work done by the resistive force is approximately -17.1 J.
Among the given options, -17.50 J (option 4) is the closest value to the calculated result.