As we know that electrostatic force is a conservative force
so we can say by the condition of conservative force
here we can rearrange the above equation as
now integrate both sides
Now we know by the definition of work done by a force is given by
now work done by conservative force is given as
Now from above work done by electric field to move charge from one point to other is given as
so here work done is given as
so change in potential energy is given by work done
Answer:
b
Explanation:
Given:
- The ball is fired at a upward initial speed v_yi = 2*v
- The ball in first experiment was fired at upward initial speed v_yi = v
- The ball in first experiment was as at position behind cart = x_1
Find:
How far behind the cart will the ball land, compared to the distance in the original experiment?
Solution:
- Assuming the ball fired follows a projectile path. We will calculate the time it takes for the ball to reach maximum height y. Using first equation of motion:
v_yf = v_yi + a*t
Where, a = -9.81 m/s^2 acceleration due to gravity
v_y,f = 0 m/s max height for both cases:
For experiment 1 case:
0 = v - 9.81*t_1
t_1 = v / 9.81
For experiment 2 case:
0 = 2*v - 9.81*t_2
t_2 = 2*v / 9.81
The total time for the journey is twice that of t for both cases:
For experiment 1 case:
T_1 = 2*t_1
T_1 = 2*v / 9.81
For experiment 2 case:
T_2 = 2*t_2
T_2 = 4*v / 9.81
- Now use 2nd equation of motion in horizontal direction for both cases:
x = v_xi*T
For experiment 1 case:
x_1 = v_x1*T_1
x_1 = v_x1*2*v / 9.81
For experiment 2 case:
x_2 = v_x2*T_2
x_2 = v_x2*4*v / 9.81
- Now the x component of the velocity for each case depends on the horizontal speed of the cart just before launching the ball. Using conservation of momentum we see that both v_x2 = v_x1 after launch. Since the masses of both ball and cart remains the same.
- Hence; take ratio of two distances x_1 and x_2:
x_2 / x_2 = v_x2*4*v / 9.81 * 9.81 / v_x1*2*v
Simplify:
x_1 / x_2 = 2
- Hence, the amount of distance traveled behind the cart in experiment 2 would be twice that of that in experiment 1.
Answer:
yeast makes the pizza dough rise
Answer:
<em>6.25</em>
Explanation:
M = d/g........................ Equation 1
making g the subject of the equation,
g = d/M............................. Equation 2
Where M = mileage per gallon, d = distance move from Essex campus to Catonsville campus, g = amount of gasoline used
<em>Given: M = 38 miles per gallon, d = 37.2 km</em>
<em>If 1 kilometer = 0.62 miles</em>
<em>Then, 37.2 km = 37.2×0.62 miles = 23.064 miles</em>
<em>Substituting these values into equation 2,</em>
<em>g = 38/23.064</em>
<em>g = 1.648 gallon</em>
<em>g ≈1.65 gallon</em>
<em>Thus, </em>
<em>If, 0.264 gallon = 1 liters.</em>
<em>Then, 1.65 gallon = 1.65×1/0.264 = 6.25 liters.</em>
<em>g = 6.25</em>
<em>Thus the car will use 6.25 liters of gasoline to move from the Essex campus to the Catonsville campus.</em>
