The coefficient of friction between the soap and the floor is 0.081
If Juan steps on the soap with a force of 493 N, this is her weight, W. This weight also equals the normal reaction on the floor, N.
We know that frictional force F = μN where μ = coefficient of friction between soap and floor.
So, μ = F/N
Since F = 40 N and N = W = 493 N,
μ = F/N
μ = 40 N/493 N
μ = 0.081
So, the coefficient of friction between the soap and the floor is 0.081
Learn more about coefficient of friction here:
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Answer:
The average induced emf around the border of the circular region is 
.
Explanation:
Given that,
Radius of circular region, r = 1.5 mm
Initial magnetic field, B = 0
Final magnetic field, B' = 1.5 T
The magnetic field is pointing upward when viewed from above, perpendicular to the circular plane in a time of 125 ms. We need to find the average induced emf around the border of the circular region. It is given by the rate of change of magnetic flux as :
So, the average induced emf around the border of the circular region is .
Answer:
3.28 m
3.28 s
Explanation:
We can adopt a system of reference with an axis along the incline, the origin being at the position of the girl and the positive X axis going up slope.
Then we know that the ball is subject to a constant acceleration of 0.25*g (2.45 m/s^2) pointing down slope. Since the acceleration is constant we can use the equation for constant acceleration:
X(t) = X0 + V0 * t + 1/2 * a * t^2
X0 = 0
V0 = 4 m/s
a = -2.45 m/s^2 (because the acceleration is down slope)
Then:
X(t) = 4*t - 1.22*t^2
And the equation for speed is:
V(t) = V0 + a * t
V(t) = 4 - 2.45 * t
If we equate this to zero we can find the moment where it stops and begins rolling down, that will be the highest point:
0 = 4 - 2.45 * t
4 = 2.45 * t
t = 1.63 s
Replacing that time on the position equation:
X(1.63) = 4 * 1.63 - 1.22 * 1.63^2 = 3.28 m
To find the time it will take to return we equate the position equation to zero:
0 = 4 * t - 1.22 * t^2
Since this is a quadratic equation it will have to answers, one will be the moment the ball was released (t = 0), the other will eb the moment when it returns:
0 = t * (4 - 1.22*t)
t1 = 0
0 = 4 - 1.22*t2
1.22 * t2 = 4
t2 = 3.28 s
Answer:
g = 11.2 m/s²
Explanation:
First, we will calculate the time period of the pendulum:
where,
T = Time period = ?
t = time taken = 135 s
n = no. of swings in given time = 98
Therefore,
T = 1.38 s
Now, we utilize the second formula for the time period of the simple pendulum, given as follows:
where,
l = length of pendulum = 54 cm = 0.54 m
g = acceleration due to gravity on the planet = ?
Therefore,
<u>g = 11.2 m/s²</u>
