An object of mass .550kg is lifted from the floor to a height of 3.5m at a constant speed. How much work is done by the lifting force (include units)?

b.) How much work is done by the Earth on the object?

c.) What is the net work done on the object?

d.) What is the change in kinetic energy of the object?

e.) Are your results consistent with the work-energy principle? Explain.

a) m g h = .55 * 9.81 * 3.5 = 18.9 Joules

b) force down, displacement up --> -18.9 J

c) the work done by the lifting force exactly matched the work done by gravity so no net work was done

d)assuming it was moving at constant speed throughout the problem, there was no change in kinetic energy.

e) the work done by our lift force exactly matched that done by gravity. If we only considered the work done by the lift force, we would say the potential energy in the gravitational field increased by m g h.

Thank You

a) The work done by the lifting force can be calculated using the formula:

Work = Force x Distance

Since the object is lifted at a constant speed, the net force acting on it is zero. Therefore, the lifting force must equal the gravitational force acting on the object, given by:

Force = mass x gravity

where mass is 0.550 kg and gravity is approximately 9.8 m/s^2.

So, the work done by the lifting force is:

Work = (0.550 kg) x (9.8 m/s^2) x (3.5 m)

b) Since the object is being lifted vertically, the force exerted by the Earth is equal in magnitude and opposite in direction to the lifting force. Therefore, the work done by the Earth on the object is equal in magnitude but opposite in sign to the work done by the lifting force.

c) The net work done on the object is the sum of the work done by the lifting force and the work done by the Earth. Since these two forces have equal magnitude but opposite signs, the net work done on the object is zero.

d) According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. Since the net work done on the object is zero, the change in kinetic energy of the object is also zero.

e) Yes, the results are consistent with the work-energy principle. The principle states that the work done on an object equals the change in its kinetic energy. In this case, since the object is lifted at a constant speed and the net work done on it is zero, the change in kinetic energy is also zero.

To calculate the work done by a lifting force, we can use the formula:

Work = Force * Distance * Cos(θ)

Given that the object is lifted at a constant speed, it means there is no acceleration, and therefore the net force acting on the object is zero. Since the lifting force counterbalances the force of gravity, the angle (θ) between the lifting force and the direction of motion is 180 degrees (or π radians). With this information, we can now proceed to answer the questions step-by-step:

a.) How much work is done by the lifting force?

The work done by the lifting force can be calculated using the formula:

Work = Force * Distance * Cos(θ)

In this case, the distance is the height through which the object is lifted, which is 3.5 meters. The force can be calculated using the formula:

Force = Mass * Acceleration due to gravity

Given that the mass of the object is 0.550 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values into the formula to find the force:

Force = 0.550 kg * 9.8 m/s^2

Now we can substitute the force and distance values into the work formula:

Work = (0.550 kg * 9.8 m/s^2) * 3.5 m * Cos(180 degrees)

Since Cos(180 degrees) = -1, we can simplify the formula:

Work = - (0.550 kg * 9.8 m/s^2) * 3.5 m

Calculating this gives us the work done by the lifting force:

Work = - (0.550 kg * 9.8 m/s^2) * 3.5 m
Work = -19.04 J

Therefore, the work done by the lifting force is -19.04 J (the negative sign indicates that the force and displacement are in the opposite direction).

b.) How much work is done by the Earth on the object?

The work done by the Earth on the object can be calculated using the same formula:

Work = Force * Distance * Cos(θ)

In this case, the force is the weight of the object, which is given by:

Force = Mass * Acceleration due to gravity

Using the same values for mass and acceleration due to gravity as before, we can find the force exerted by the Earth:

Force = 0.550 kg * 9.8 m/s^2

Now we can substitute the force and distance values into the work formula:

Work = (0.550 kg * 9.8 m/s^2) * 3.5 m * Cos(0 degrees)

Since Cos(0 degrees) = 1, we can simplify the formula:

Work = (0.550 kg * 9.8 m/s^2) * 3.5 m

Calculating this gives us the work done by the Earth on the object:

Work = (0.550 kg * 9.8 m/s^2) * 3.5 m
Work = 19.04 J

Therefore, the work done by the Earth on the object is 19.04 J.

c.) What is the net work done on the object?

The net work done on the object is the sum of the work done by the lifting force and the work done by the Earth. Since the work done by the lifting force is negative and the work done by the Earth is positive, we can calculate the net work as follows:

Net work = Work done by the lifting force + Work done by the Earth
Net work = -19.04 J + 19.04 J
Net work = 0 J

Therefore, the net work done on the object is 0 J.

d.) What is the change in kinetic energy of the object?

According to the work-energy principle, the net work done on an object is equal to the change in its kinetic energy. Since the net work done on the object is 0 J (as calculated in the previous step), it means that there is no change in the kinetic energy of the object.

e.) Are your results consistent with the work-energy principle? Explain.

Yes, the results are consistent with the work-energy principle. According to the work-energy principle, the net work done on an object is equal to the change in its kinetic energy. In this case, the net work done on the object is 0 J, which means there is no change in its kinetic energy. This is supported by the fact that the object is lifted at a constant speed, indicating that there is no change in its kinetic energy. Therefore, the results are consistent with the work-energy principle.

To find the answers to these questions, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. We can break down these questions one by one.

a) How much work is done by the lifting force?
The work done by a force is given by the equation:
Work = Force × Distance × Cosine(angle between force and displacement)

Since the object is lifted at a constant speed, the net force acting on it must be zero. This means that the lifting force must be equal in magnitude but opposite in direction to the gravitational force acting on the object (weight). Therefore, the angle between the lifting force and the displacement is 180 degrees, and the cosine of 180 degrees is -1.

The work done by a force can also be calculated as the product of the force and the displacement (∆x).
So, for a constant speed, the work done by the lifting force is:
Work = Force × Distance × -1 = -mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

Plugging in the given values:
Work = -(0.550 kg) × (9.8 m/s^2) × (3.5 m) = -19.49 Joules

Note: The negative sign indicates that the work done by the lifting force is negative because the force is in the opposite direction of the displacement.

b) How much work is done by the Earth on the object?
Since the object is lifted at a constant speed, the net force acting on it is zero. This means that the work done by the Earth on the object is zero. The Earth's gravitational force does not perform any work on the object in this case.

Work = 0 Joules

c) What is the net work done on the object?
The net work done on the object is the sum of the work done by all the forces acting on it. In this case, the only force we considered was the lifting force, and it had a work of -19.49 Joules. Therefore, the net work done on the object is also -19.49 Joules.

Net Work = -19.49 Joules

d) What is the change in kinetic energy of the object?
According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. Since there is no mention of the object's initial or final velocities, we can assume that the object starts and ends at rest. Therefore, the initial and final kinetic energies are both zero.

Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Change in Kinetic Energy = 0 - 0
Change in Kinetic Energy = 0 Joules

e) Are your results consistent with the work-energy principle? Explain.
Yes, the results are consistent with the work-energy principle. The net work done on the object (-19.49 Joules) is zero because there is no change in the object's kinetic energy. This is consistent with the principle since the object was lifted at a constant speed, meaning there was no transfer of mechanical energy to or from the object.