a person in a wheelchair with a total mass of 100 kg is pushed from rest to a speed of 2.0m/s. if the effective coefficient of friction is .05 and the distance moved is 15 m calculate the work done, calculate the average force that must be exerted on the wheelchair to accomplish this
Well, it seems like this wheelchair situation is rolling towards some physics calculations. Hold on tight, here we go!
To calculate the work done, we need to find the force experienced by the wheelchair. We're given the coefficient of friction and the mass of the person in the wheelchair. The formula we can use here is:
Work = Force × Distance
Now, let's find the force first. The frictional force can be calculated using:
Frictional Force = Coefficient of Friction × Normal Force
The normal force is equal to the weight of the person in the wheelchair, which is given by:
Normal Force = Mass × Gravitational Acceleration
Combining all of this, we can say:
Frictional Force = (Coefficient of Friction) × (Mass × Gravitational Acceleration)
Next, we'll calculate the work done:
Work = Frictional Force × Distance
Now, let's plug in the given values and do the math!
Mass = 100 kg
Coefficient of Friction = 0.05
Distance = 15 m
Gravitational Acceleration (approx.) = 9.8 m/s²
First, we find the normal force:
Normal Force = (Mass) × (Gravitational Acceleration)
Normal Force = 100 kg × 9.8 m/s²
Normal Force = 980 N
Now, let's determine the frictional force:
Frictional Force = (Coefficient of Friction) × (Normal Force)
Frictional Force = 0.05 × 980 N
Frictional Force = 49 N
Finally, we can find the work done:
Work = Frictional Force × Distance
Work = 49 N × 15 m
Work ≈ 735 J
So, the work done to push the person in the wheelchair from rest to a speed of 2.0 m/s is approximately 735 Joules.
Now, calculating the average force involved is a piece of 🎂!
Average Force = Work ÷ Distance
Average Force = 735 J ÷ 15 m
Average Force ≈ 49 N
So, the average force that must be exerted on the wheelchair to accomplish this is approximately 49 Newtons. Keep in mind, these calculations are just estimates and might have some rounding errors, but they should give you a good laugh... I mean, understanding!
To calculate the work done to push the person in a wheelchair, we can use the formula:
Work = Force * Distance
First, let's calculate the force required to move the wheelchair:
Frictional Force = coefficient of friction * Normal Force
The normal force is the weight of the person in the wheelchair:
Weight = mass * gravity
Normal Force = Weight - Force of gravity
= mass * gravity - mg
Now, let's calculate the force of gravity:
Force of gravity = mass * gravity
Next, let's calculate the average force needed to push the wheelchair:
Average Force = Work / Distance
Let's plug in the values and calculate step-by-step:
1. Calculate the force of gravity:
Force of gravity = mass * gravity
= 100 kg * 9.8 m/s²
= 980 N
2. Calculate the normal force:
Normal Force = Weight - Force of gravity
= 100 kg * 9.8 m/s² - 980 N
= 0 N
3. Calculate the frictional force:
Frictional Force = coefficient of friction * Normal Force
= 0.05 * 0 N
= 0 N
4. Calculate the work done:
Work = Force * Distance
= Frictional Force * Distance
= 0 N * 15 m
= 0 J
5. Calculate the average force:
Average Force = Work / Distance
= 0 J / 15 m
= 0 N
Therefore, the work done to push the person in the wheelchair is 0 J, and the average force required to push the wheelchair is 0 N.
To calculate the work done on the wheelchair and the average force exerted, you can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to its change in kinetic energy.
1. Calculate the change in kinetic energy:
The initial kinetic energy of the wheelchair is zero as it starts from rest. The final kinetic energy can be calculated using the mass and speed given. The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * speed^2
Substituting the given values:
Initial Kinetic Energy = 0
Final Kinetic Energy = (1/2) * 100 kg * (2.0 m/s)^2
2. Calculate the work done:
The work done on the wheelchair is equal to the change in kinetic energy. Therefore:
Work Done = Final Kinetic Energy - Initial Kinetic Energy
3. Calculate the average force:
The average force exerted on the wheelchair can be calculated using the formula:
Work Done = Average Force * Distance
Rearrange the formula to solve for Average Force:
Average Force = Work Done / Distance
Substitute the calculated Work Done and the given Distance to find the Average Force.
Now let's calculate the values:
1. Calculate the final kinetic energy:
Final Kinetic Energy = (1/2) * 100 kg * (2.0 m/s)^2
2. Calculate the work done:
Work Done = Final Kinetic Energy - Initial Kinetic Energy
= Final Kinetic Energy - 0
3. Calculate the average force:
Average Force = Work Done / Distance
Substitute the values into the formulas to calculate the answers.
Vf^2=vi^2+2ad
but a= net force/mass=(pushing force-mg*.05)mass
a= force/mass -.05g
2^2=2*(force/100 - .05g)*15
solve for force.