The tops of the towers of the golden gate bridge in san Francisco, are 227m above the water. suppose a worker drops a 655g wrench from the top of a tower. if the average force of air resistance is 2.20 percent of the force of free fall what will the kinetic energy of the wrench be when it hits the water?
To calculate the kinetic energy of the wrench when it hits the water, we need to find the final velocity of the wrench just before impact. We can use the principles of free fall and take into account the force of air resistance.
First, let's calculate the height from which the wrench is dropped:
Height = 227m
Next, we'll find the gravitational potential energy of the wrench at that height. The potential energy is equal to the work done on the wrench when it's lifted to that height:
Potential energy = mass x gravity x height
= 0.655kg x 9.8m/s^2 x 227m
Next, let's calculate the force of air resistance on the wrench:
Force of air resistance = 2.20% of force of free fall
The force of free fall is equal to the weight of the wrench:
Force of free fall = mass x gravity
= 0.655kg x 9.8m/s^2
Now let's calculate the magnitude of the force of air resistance:
Force of air resistance = 0.022 x Force of free fall
Next, we'll calculate the deceleration due to air resistance. Since the force of air resistance opposes the motion, it acts in the opposite direction to the gravitational force. Therefore, the net force acting on the wrench is:
Net force = Force of free fall - Force of air resistance
Next, we'll use Newton's second law to find the deceleration:
Deceleration = Net force / mass
Finally, we can calculate the final velocity of the wrench using the following kinematic equation:
Final velocity^2 = Initial velocity^2 + 2 x acceleration x distance
Since the initial velocity is zero when the wrench is dropped, the equation simplifies to:
Final velocity^2 = 0 + 2 x acceleration x distance
Using the height of the tower as the distance, plug in the values to find the final velocity.
Once we have the final velocity, the kinetic energy of the wrench just before hitting the water is given by:
Kinetic energy = 0.5 x mass x (final velocity)^2
Please note that due to rounding errors and specific values used in calculations, the final answer may slightly vary.
To calculate the kinetic energy of the wrench when it hits the water, we need to take into account the gravitational potential energy it initially has and the work done against air resistance during its fall.
First, let's determine the gravitational potential energy (GPE) of the wrench at the top of the tower. The GPE is given by the formula:
GPE = m × g × h
Where:
m = mass of the wrench = 0.655 kg (converted from 655g)
g = acceleration due to gravity = 9.8 m/s²
h = height above the water = 227 m
Plugging in these values, we get:
GPE = 0.655 kg × 9.8 m/s² × 227 m
Next, we need to account for the work done against air resistance during the wrench's fall. The force of air resistance is given as 2.20 percent of the force of free fall.
The force of free fall is equal to the weight of the object, which can be calculated as:
Weight = m × g
To find the force of air resistance, we multiply the force of free fall by 2.20 percent:
Force of air resistance = 0.022 × Weight
Now, let's calculate the work done against air resistance. The work done is given by the formula:
Work = Force × Distance
In this case, the distance is the height of the tower, and the force is the force of air resistance. Plugging in the values, we get:
Work = Force of air resistance × h
Next, we need to subtract the work done against air resistance from the initial gravitational potential energy to find the final kinetic energy when it hits the water.
Kinetic Energy = GPE - Work
Plugging in the values and calculating, we can find the final kinetic energy of the wrench when it hits the water.
I suppose that what they are calling the "force of free fall" is the weight, M g.
Frictional work performed against air resistance while falling will then be
0.022 M g H
Subtract that from M g H to get the kinetic energy when it hits the water.
(1/2) M V^2 = 0.978 M g H