You observe someone pulling a block of mass 48 kg across a low-friction surface. While they pull a distance of 3.0 m in the direction of motion, the speed of the block changes from 4.9 m/s to 7.7 m/s.
Calculate the magnitude of the force exerted by the person on the block.
This I figured out using moment principle and the position update formula. 282 N.
What was the change in internal energy (chemical plus thermal) of the person pulling the block?
How do I get this? I know that DEtot = q + W, I can find W and Kinetic energy. but what other energies would be included in Ei and Ef?
Also, I know the rest energies would cancel out.
Well, to calculate the change in internal energy (DEtot) of the person pulling the block, you'll need to consider the different types of energy involved.
DEtot = Ef - Ei
Let's break it down:
1. Kinetic Energy (KE): This is the energy associated with the person's movement. You can calculate the initial and final kinetic energies using the formula KE = 0.5 * mass * velocity^2.
2. Work done (W): You already mentioned that you can calculate this, and it represents the work done by the person in pulling the block.
3. Chemical Energy (CE): This refers to the potential energy stored in the person's body due to the chemical reactions happening within. It's a bit tricky to determine the exact change in chemical energy, as it depends on various factors like food intake, metabolism, etc. We'll assume it remains constant for simplicity.
4. Thermal Energy (TE): This represents any heat energy generated during the activity. Again, it's difficult to determine the exact value without additional information.
So, in this case, you can consider the change in internal energy (DEtot) to be primarily due to work done (W) and a negligible change in chemical energy (CE). As for thermal energy (TE), we don't have enough information to calculate it accurately.
Therefore, based on the limited information provided, you can calculate the change in internal energy by using the formula:
DEtot = W + CE + TE
However, since CE and TE are negligible in this scenario, you can simplify it to:
DEtot ≈ W
I hope that helps! Remember, when it comes to energy calculations, it's important to consider all the different factors at play, or at least make suitable assumptions when information is missing.
To calculate the change in internal energy (DEtot) of the person pulling the block, we need to consider the work done (W) and the change in kinetic energy (DEk) of the person.
The equation DEtot = q + W relates the change in internal energy (DEtot) to the heat transfer (q) and the work done (W), but in this case, we are not given any information about heat transfer, so we can ignore the q term.
So we only need to consider the work done (W) and the change in kinetic energy (DEk) of the person.
The work done (W) is given by the equation:
W = F * d * cosθ
Where F is the force exerted by the person on the block, d is the distance over which the force is exerted, and θ is the angle between the force and the displacement. In this case, the force is parallel to the displacement, so θ = 0°, and cosθ = 1. The force (F) can be calculated using Newton's second law:
F = m * a
Where m is the mass of the block and a is the acceleration. In this case, we can use the formula for calculating average acceleration:
a = (vf - vi) / t
Where vf is the final velocity, vi is the initial velocity, and t is the time taken. Given that the distance (d) and time (t) are already given, we can calculate the initial velocity (vi) and final velocity (vf) using the formulas:
vi = (2 * d - vf * t) / t
vf = (2 * d - vi * t) / t
Now we can calculate the force (F) using the formula:
F = m * a
Next, we need to calculate the change in kinetic energy (DEk) of the person. The change in kinetic energy is given by the equation:
DEk = 1/2 * m * (vf^2 - vi^2)
Where m is the mass of the person and vf and vi are the final and initial velocities of the person, respectively.
To calculate the final and initial velocities of the person, we can use the following formulas:
vf = (2 * d - vi * t) / t
vi = (2 * d - vf * t) / t
Now we can substitute the values into the equation to calculate DEk.
Finally, the change in internal energy (DEtot) is given by the equation:
DEtot = W + DEk
Now you can calculate the change in internal energy (DEtot) of the person pulling the block.
To calculate the change in internal energy of the person pulling the block, we first need to understand what energies are involved. In this case, we can assume that the only relevant energies are the mechanical energy associated with the block and the work done by the person.
First, let's calculate the work done by the person. The work done is equal to the force exerted multiplied by the distance over which it is exerted. In this case, the force exerted is the magnitude of the force you calculated earlier, which is 282 N, and the distance is 3.0 m. So, the work done by the person is:
W = force x distance
= 282 N x 3.0 m
= 846 J
Next, let's calculate the change in mechanical energy of the block. The mechanical energy is the sum of the kinetic energy before and after the pull. The kinetic energy is given by the equation:
KE = (1/2) x mass x velocity^2
Before the pull, the kinetic energy is:
KEi = (1/2) x mass x velocityi^2
= (1/2) x 48 kg x (4.9 m/s)^2
= 563.28 J
After the pull, the kinetic energy is:
KEf = (1/2) x mass x velocityf^2
= (1/2) x 48 kg x (7.7 m/s)^2
= 1768.8 J
The change in mechanical energy is:
ΔKE = KEf - KEi
= 1768.8 J - 563.28 J
= 1205.52 J
Finally, let's calculate the change in internal energy. The change in internal energy (ΔEtot) is equal to the sum of the heat transferred (q) and the work done (W). In this case, no heat transfer is mentioned, so we only have the work done. Therefore, the change in internal energy is:
ΔEtot = q + W
= 0 + 846 J
= 846 J
Therefore, the change in internal energy of the person pulling the block is 846 J.