suppose the glider is initially at rest at x=0, with the spring unstretched. You then apply a constant force in the +x direction with magnitude 0.610 N to the glider. what is the glider's velocity when it has moved 0.100m?
To find the glider's velocity when it has moved 0.100 m, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a), or F = ma.
In this case, we know that a constant force of magnitude 0.610 N is applied in the +x direction to the glider. Since the force is constant, the acceleration of the glider will also be constant.
To find the acceleration, we need to know the mass of the glider. Let's assume the mass of the glider is represented by 'm' (in kg).
From Newton's second law, we can rearrange the equation to solve for acceleration:
a = F/m
Substituting the given values, we have:
a = 0.610 N / m
Now, we need to determine the time it takes for the glider to move 0.100 m. We can use one of the equations of motion:
x = ut + (1/2)at^2
In this equation, x represents the displacement (0.100 m), u represents the initial velocity (0 m/s), a represents the acceleration, and t represents the time.
Since the glider is initially at rest, the initial velocity (u) is 0 m/s. Rearranging the equation, we have:
t = sqrt((2x)/a)
Now, we can substitute the given values into the equation to find the time:
t = sqrt((2 * 0.100 m) / (0.610 N / m))
Simplifying, we get:
t = sqrt(0.3279 / (0.610 N / m))
t = sqrt(0.3279 * (m / 0.610 N))
t = sqrt(0.5366 * m / N)
t = sqrt(0.5366 * m) / sqrt(N)
Now, we have the time it takes for the glider to move 0.100 m. To find the velocity, we can use another equation of motion:
v = u + at
Since the glider is initially at rest (u = 0 m/s), the equation becomes:
v = at
Substituting in the values, we get:
v = (0.610 N / m) * (sqrt(0.5366 * m) / sqrt(N))
Simplifying, we get:
v = (0.610 N * sqrt(0.5366 * m)) / (m * sqrt(N))
Therefore, the glider's velocity when it has moved 0.100 m is given by this equation.