M= gpe / gh
G= gpe / mh
H=gpe / mg
Answer:
See the answers below.
Explanation:
We will solve this problem by calculating each part separately.
A 500 W hair dyer is used to dry hair for 6 minutes a day for 3 days.
Energy can be calculated by multiplying the value of the power of the equipment by the amount of time of use.
![500 [W]*[\frac{6min}{1day} ]*[\frac{1day}{24hr} ]*[\frac{1hr}{60min} ]=2.083 [W]](https://tex.z-dn.net/?f=500%20%5BW%5D%2A%5B%5Cfrac%7B6min%7D%7B1day%7D%20%5D%2A%5B%5Cfrac%7B1day%7D%7B24hr%7D%20%5D%2A%5B%5Cfrac%7B1hr%7D%7B60min%7D%20%5D%3D2.083%20%5BW%5D)
The cots of electricity is 5.6 cents per kWh. How much would it cost to operate the laptop for 24 hours a day for one week?
We know that the power of the latop is 75 [W], then we can calculate the cost, multiplying the value of the power by the value of the cost by the time of use of the computer.
![0.075[kW]*5.6[\frac{cents}{kw*h}}]*[\frac{24hr}{1day}]*[1week]*[\frac{7days}{1week} ]=70.56 [cents]](https://tex.z-dn.net/?f=0.075%5BkW%5D%2A5.6%5B%5Cfrac%7Bcents%7D%7Bkw%2Ah%7D%7D%5D%2A%5B%5Cfrac%7B24hr%7D%7B1day%7D%5D%2A%5B1week%5D%2A%5B%5Cfrac%7B7days%7D%7B1week%7D%20%5D%3D70.56%20%5Bcents%5D)
A toaster oven is 85% efficient. It uses 1200 J of energy. How much thermal energy is it producing?
Efficiency is defined as the relationship between the energy obtained on the energy delivered. Almost always the energy delivered is greater than the energy obtained (first law of thermodynamics).
Therefore.
![Effic = E_{obtained}/E_{delivered}\\0.85=E_{obtained}/1200\\E_{obtained}=1020[J]](https://tex.z-dn.net/?f=Effic%20%3D%20E_%7Bobtained%7D%2FE_%7Bdelivered%7D%5C%5C0.85%3DE_%7Bobtained%7D%2F1200%5C%5CE_%7Bobtained%7D%3D1020%5BJ%5D)
The kinetic energy of any moving object is
K.E. = (1/2) (mass) (speed)² .
To use this simple formula, the 'mass' has to be in kilograms,
and the 'speed' has to be in meters-per-second.
You can see that we have a slight problem that has to be cleaned up:
The speed in the question is given in "kilometers per hour", but we'll
need it in "meters per second". So let's convert that right now:
(600 km/hour) x (1 hour / 3600 seconds) x (1000 meters / km)
= (600 x 1 x 1000 / 3600) (km-hour-meters / hour-second-km)
= 166.67 meters/second .
Now we're ready to plug numbers into the formula for K.E.
(1/2) (mass) (speed)²
= (1/2) (80,000 kg) (166.67 m/s)²
= (40,000 kg) (27,777.8 m²/s²)
= 1,111,111,111 kg-m²/s²
= 1.1... x 10⁹ Joules (choice D)
Answer:
0.9432 m/s
Explanation:
We are given;
Mass of swimmer;m_s = 64.38 kg
Mass of log; m_l = 237 kg
Velocity of swimmer; v_s = 3.472 m/s
Now, if we consider the first log and the swimmer as our system, then the force between the swimmer and the log and the log and the swimmer are internal forces. Thus, there are no external forces and therefore momentum must be conserved.
So;
Initial momentum = final momentum
m_l × v_l = m_s × v_s
Where v_l is speed of the log relative to water
Making v_l the subject, we have;
v_l = (m_s × v_s)/m_l
Plugging in the relevant values, we have;
v_l = (64.38 × 3.472)/237
v_l = 0.9432 m/s
Answer:

Explanation:
In this case we have to work with vectors. Firs of all we have to compute the angles between x axis and the r vector (which points the charges):

the electric field has two components Ex and Ey. By considering the sign of the charges we obtain that:

Hence, by replacing E1 and E2 we obtain:
![\vec{E}=[(68.67N/C)cos(90\°)-(16.52N/C)cos(17.10\°)]\hat{i}+[(68.67N/C)sin(90\°)-(16.52N/C)sin(17.10\°)]\hat{j}\\\\\vec{E}=(-15.78\hat{i}+63.81\hat{j})\frac{N}{C}](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%3D%5B%2868.67N%2FC%29cos%2890%5C%C2%B0%29-%2816.52N%2FC%29cos%2817.10%5C%C2%B0%29%5D%5Chat%7Bi%7D%2B%5B%2868.67N%2FC%29sin%2890%5C%C2%B0%29-%2816.52N%2FC%29sin%2817.10%5C%C2%B0%29%5D%5Chat%7Bj%7D%5C%5C%5C%5C%5Cvec%7BE%7D%3D%28-15.78%5Chat%7Bi%7D%2B63.81%5Chat%7Bj%7D%29%5Cfrac%7BN%7D%7BC%7D)
hope this helps!!