Answer:
The ratio of mass that is discarded is determined by this equation:
M - m = (3a/2)/(g²- (a²/2) - (ag/2))
Explanation:
The force acting on an object in motion is defined by the equation:
F = ma
Additionally, there is a gravitational force consistently acting downwards on the object, defined as g = 9.8 ms⁻²
For convenience, we will utilize a positive notation for downward acceleration and a negative notation for upward acceleration.
Case 1:
The hot air balloon has mass = M
Acceleration = a
Upward thrust from hot air = F = constant
Gravitational force acting downward = Mg
The net force on the balloon can be expressed as:
Ma = Gravitational force - Upward Force
Ma = Mg - F (since the balloon moves downward, that means Mg > F)
F = Mg - Ma
F = M (g-a)
M = F/(g-a)
Case 2:
After releasing the ballast, the new mass becomes m. The new upward acceleration is -a/2:
The net force is expressed as:
-m(a/2) = mg - F (The balloon is moving upwards, hence F > mg)
F = mg + m(a/2)
F = m(g + (a/2))
m = F/(g + (a/2))
Determining the fraction of the mass initially dropped:
Answer:
The pen requires 7.2 mJ of energy to extend.
Explanation:
Provided:
Length = 1.8 cm
Spring constant = 300 N/m
Initial compression = 1.0 mm
Additional compression = 6.0 mm
Total compression = 1.0 + 6.0 = 7.0 mm
We need to determine the energy needed
This energy is equivalent to the variation in spring potential energy
Substitute the values into the formula
Therefore, a total of 7.2 mJ is needed to extend the pen.
Complete Question
An aluminum "12 gauge" wire measures a diameter of 0.205 centimeters. The resistivity ρ of aluminum is 2.75×10−8 ohm-meters. The electric field E in the wire varies over time as E(t)=0.0004t2−0.0001t+0.0004 newtons per coulomb, where time is recorded in seconds.
At time 5 seconds, I = 1.2 A.
We need to find the charge Q traveling through a cross-section of the conductor from time 0 to time 5 seconds.
Answer:
The charge is
Explanation:
The question indicates that
The wire’s diameter is
The radius of the wire is
Aluminum's resistivity is
The electric field variation is described as
The charge is effectively given by the equation
Where A is the area expressed as
Thus,
Therefore
By substituting values
The question states that t = 5 seconds
Response:D
Clarification:
Provided
mass of object
Distance traveled
resulting velocity
energy conservation occurs starting when the object begins its descent and reaches a speed of 12 m/s
Initial Energy
Final Energy
where is the work done by friction, if any
As friction is present, this indicates an open system with a net external force of zero.
An open system allows for the exchange of energy and mass, and the presence of friction indicates that it is indeed an open system.