If gear a rotates with a constant angular acceleration of aa = 90 rad>s2, starting from rest, determine the time required for gear d to attain an angular velocity of 600 rpm. Also, find the number of revolutions of gear d to attain this angular velocity. Gears a, b, c, and d have radii of 15 mm, 50 mm, 25 mm, and 75 mm, respectively.
What is the revolution ratio of two spur gears with one having 12 teeth and the other having 36 teeth
3:1 is the ratio i hope this belps
You say goodbye to your friend at the intersection of two perpendicular roads. At time t=0 you drive off North at a (constant) speed v and your friend drives West at a (constant) speed ????. You badly want to know: how fast is the distance between you and your friend increasing at time t?
Rate of Change
When an object moves at constant speed v, the distance traveled at time t is
We know at time t=0 two friends are at the intersection of two perpendicular roads. One of them goes north at speed v and the other goes west at constant speed w (assumed). Since both directions are perpendicular, the distances make a right triangle. The vertical distance is
and the horizontal distance is
The distance between both friends is computed as the hypotenuse of the triangle
We need to find d', the rate of change of the distance between both friends.
Plugging in the above relations
Solving for d
Differentiating with respect to t
The problem is solved using Pythagoras' Theorem, representing the two travel paths forming a right triangle. The rate at which the distance increases between two points moving perpendicularly can be found by differentiating the resulting equation, which yields the expression sqrt[(v^2)+(u^2)].
The question is about the rate at which the distance between you and your friend is increasing at time t. It's a typical problem in kinematics. Because the roads are perpendicular to each other, we can solve the problem using Pythagoras' Theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's denote the distance you've traveled as D1 = v*t (because distance = speed * time) and the distance your friend has travelled D2 = u*t. The distance between you can be computed using Pythagoras' Theorem as D = sqrt(D1^2 + D2^2). Hence, D = sqrt[(v*t)^2 + (u*t)^2]. Differentiating D with respect to t using the chain rule will give us the rate at which the distance between you is increasing, which is sqrt[(v^2)+(u^2)].
John and Suzie are trying to improve the speed of their race car by adjusting the angle of the rear spoiler. Which choice is the controlled variable(s)?the maximum speed and the angle of the rear spoiler
the type of tire and the type of fuel
only the maximum speed
only the angle of the rear spoiler
the type of tire and the type of fuel
Students have four identical, hollow, uncharged conducting spheres, W, X, Y, and Z.Sphere Z is given a positive charge of +40 C. Sphere Z is touched first to sphere W, then sphere X, and finally to sphere Y. What is the resulting charge on sphere Y?
a. +5 με
b. +10 μC
c. +20 μC
d. +40 με
because they made contact that means their new force will be the same
Sphere Z is initially charged with +40 C. When it is touched to three other spheres, the charge is evenly distributed among them. The resulting charge on sphere Y is +10 μC.
The initial charge on sphere Z is +40 C. When sphere Z is touched to sphere W, the charge is evenly distributed between the two spheres, resulting in each sphere having a charge of +20 C. Then, when sphere Z is touched to sphere X, the total charge is evenly distributed between all three spheres, resulting in each sphere having a charge of +13.33 C. Finally, when sphere Z is touched to sphere Y, the total charge is evenly distributed between all four spheres, resulting in each sphere having a charge of +10 C. Therefore, the resulting charge on sphere Y is +10 μC (option b).
￼true or false A permanent magnet and a coil of wire carrying a current both produce magnetic fields
True. A permanent magnet like the earth produces its own B field due to movement of the iron core. The earths magnetic field is the reason why we have an atmosphere and it also is the only defense against solar flares. A coil of wire or solenoid that has current have so much moving charge that the motion of the electrical charge can create a significant G b-field
At what temperature will silver have a resistivity that is two times the resistivity of iron at room temperature? (Assume room temperature is 20° C.)
The temperature of silver at this given resistivity is 2971.1 ⁰C
The resistivity of silver is calculated as follows;
Rt is the resistivity of silver at the given temperature
Ro is the resistivity of silver at room temperature
α is the temperature coefficient of resistance
To is the room temperature
T is the temperature at which the resistivity of silver will be two times the resistivity of iron at room temperature
Resistivity of iron at room temperature = 9.71 x 10⁻⁸ ohm.m
When silver's resistivity becomes 2 times the resistivity of iron, we will have the following equations;
Therefore, the temperature of silver at this given resistivity is 2971.1 ⁰C