a person horizontally pushes a 25 kg couch. Applied force is 18N and average resistive force is 7N. its pushed from rest to a final speed of 2.3
what is the distance pushed
the time taken
and the power delivered to push couch
net push = 18 - 7 = 11 N
so
11 = m a = 25 a
so
a = 11/25 m/s^2
v = a t
so t = 2.3 * 25/11 = 5.23 s
and
average v = (0+2.3)/2 = 1.15 m/s
so
d = 1.15 * 5.23 = 6.01 meters
power = force * distance/ime
= 18 *6.01/5.23 = 20.7 Joules average power
wouldn't time be 2.3 times 11/25 then?
thank you
To find the distance pushed, time taken, and power delivered to push the couch, we can use Newton's second law of motion, the equation for work, and the equation for power.
1. Distance Pushed:
The work done on an object can be calculated using the formula:
Work = Force x Distance
In this case, the applied force and the resistive force are in opposite directions. The net force can be calculated by subtracting the resistive force from the applied force:
Net Force = Applied Force - Resistive Force
Using the formula for work, we can rearrange it to solve for distance:
Distance = Work / Net Force
Given that the applied force is 18N and the resistive force is 7N, the net force can be calculated as:
Net Force = 18N - 7N = 11N
Substituting the given values, we can calculate the distance:
Distance = Work / Net Force = ??? / 11N
To find the work done, we need to calculate the change in kinetic energy of the couch. The formula for kinetic energy is:
Kinetic Energy = 1/2 * Mass * Velocity^2
Initially, the couch is at rest (velocity = 0), so the initial kinetic energy is 0.
At the final speed of 2.3 m/s, the kinetic energy is:
Final Kinetic Energy = 1/2 * Mass * (Velocity)^2 = 1/2 * 25 kg * (2.3 m/s)^2
The work done on the couch is the change in kinetic energy:
Work = Final Kinetic Energy - Initial Kinetic Energy = 1/2 * 25 kg * (2.3 m/s)^2 - 0
Now, we can substitute the calculated work into the distance formula to find the distance pushed:
Distance = Work / Net Force = (1/2 * 25 kg * (2.3 m/s)^2 - 0) / 11N
Performing the calculations will give you the distance pushed.
2. Time Taken:
To find the time taken, we'll use the equation of motion:
Distance = (Initial Velocity * Time) + (1/2 * Acceleration * Time^2)
In this case, the couch starts from rest (initial velocity = 0), and we can assume constant acceleration.
The distance pushed can be substituted into the equation as the "Distance" term, and rearranging it will give us the equation to calculate the time taken:
Time = sqrt((2 * Distance) / Acceleration)
Given that we've already calculated the distance, we can substitute its value into the equation and solve for the time taken.
Note: The acceleration will be the net force divided by the mass of the couch:
Acceleration = Net Force / Mass
Substituting the values and performing the calculations will give you the time taken.
3. Power Delivered:
Power is the rate at which work is done. It can be calculated using the formula:
Power = Work / Time
Given that we've already calculated the work and time, we can substitute their values into the equation to find the power delivered to push the couch.
Performing the calculations as described will provide the answers to the distance pushed, time taken, and power delivered.