Two cars of equal mass are traveling as shown in the figure below just before undergoing a collision. Before the collision, one of the cars has a speed of 19 m/s along +x, and the other has a speed of 31 m/s along +y. The cars lock bumpers and then slide away together after the collision. What are the magnitude and direction of their final velocity?
Momentum is conserved (always).
Final Vx = 9.5 m/s (for equal masses)
Final Vy = 15.5 m/s (for equal masses)
Use the Pythagorean theorem for magnitude.
Direction = arctan 31/19 = 58.5 degrees from +x axis, towards +y
The electronic flash attachment for a camera contains a capacitor for storing the energy used to produce the flash. In one such unit, the potential difference between the plates of a 775 µF capacitor is 330 V.
(a) Determine the energy that is used to produce the flash in this unit.
(b) Assuming that the flash lasts for 5.0*10^-3 s, find the effective power or "wattage" of the flash.
So far:
0.000775 Farads= Coulumbs / 330V
Coulumbs=0.25575C
Now here I'm not sure what to do next.
But I push on:
1A=1C/s
So:
0.25575C/5x10^-3s=51.15A
P=IV
P=51.15A*330V=16879.5W
But, that answer is kicked backed as wrong, and I'm not quite sure how to go about part A.
oops. sorry. messed that up didn't i?
To find the magnitude and direction of their final velocity, we can use the principles of conservation of linear momentum and the Pythagorean theorem.
1. Conservation of linear momentum states that the total linear momentum before the collision is equal to the total linear momentum after the collision, given that no external forces act on the system.
Let's denote the mass of each car as 'm', the initial velocities as 'v1' and 'v2', and the final velocities as 'V1' and 'V2'.
The total linear momentum before the collision is:
Initial momentum = m * v1 + m * v2
2. After the collision, the two cars lock bumpers and slide away together. This means they have the same final velocity.
So, V1 = V2 = V
3. To determine the magnitude and direction of the final velocity, we can use the Pythagorean theorem.
The magnitude of the final velocity (V) can be calculated as:
V = √(Vx^2 + Vy^2)
Where Vx and Vy are the x-component and y-component of the final velocity.
Now, let's calculate the magnitude and direction of the final velocity:
Given:
m = mass of each car
v1 = 19 m/s along +x
v2 = 31 m/s along +y
Step 1:
Initial momentum = m * v1 + m * v2
Step 2:
Since the cars lock bumpers and slide away together, V1 = V2 = V
Step 3:
To calculate the magnitude of the final velocity V, we need to find Vx and Vy.
Vx = Final x-component velocity = V = ?
Vy = Final y-component velocity = V = ?
To find Vx, we can use the conservation of momentum along the x-axis:
m * v1 = m * Vx
Vx = v1
To find Vy, we can use the conservation of momentum along the y-axis:
m * v2 = m * Vy
Vy = v2
Now, we can calculate the magnitude of the final velocity V:
V = √(Vx^2 + Vy^2)
Plug in the values:
V = √(v1^2 + v2^2)
After calculating V, we can find the direction of the final velocity using trigonometry:
tan(θ) = Vy / Vx
Therefore:
1. Calculate Vx = v1
2. Calculate Vy = v2
3. Calculate V = √(Vx^2 + Vy^2)
4. Calculate θ = arctan(Vy / Vx)
The magnitude of the final velocity V is the answer to the first part of the question, and the direction θ gives the direction of the final velocity.