when a block is pulled out to x=+4.0cm, we must apply a force amgnitude 360N to hold it there. we pull the block to x=11cm and then realease it. how much work does the spring do on the block as the block moves from xi=+5.0cm to a)x=+3.0cm, b)x=-3.0cm, c)x=-5.0cm, d)x=-9.0cm?
A force of ion stretches a wire thou 3.0cm.ldh force will stretch it through 5.0cm and through what length will a force of 100n stretch it ?what assumption have you made
To find the work done by the spring as the block moves from one position to another, we can use the formula:
Work = (1/2) * k * delta_x^2
Where:
- Work is the work done by the spring.
- k is the spring constant.
- delta_x is the displacement of the block.
In this case, we are given that the force applied to hold the block at x = +4.0 cm is 360 N. Since the force applied to hold the block in place is equal to the force exerted by the spring, we can use Hooke's Law to find the spring constant (k):
F = k * delta_x
Now, let's solve for k:
360 N = k * 4.0 cm
k = 360 N / 4.0 cm
k = 90 N/cm
Now that we have the spring constant, we can calculate the work done by the spring for each given displacement.
a) For x = +3.0 cm:
delta_x = 3.0 cm - 5.0 cm = -2.0 cm (negative because we're moving to the left)
Work = (1/2) * (90 N/cm) * (-2.0 cm)^2
b) For x = -3.0 cm:
delta_x = -3.0 cm - 5.0 cm = -8.0 cm (negative because we're moving to the left)
Work = (1/2) * (90 N/cm) * (-8.0 cm)^2
c) For x = -5.0 cm:
delta_x = -5.0 cm - 5.0 cm = -10.0 cm (negative because we're moving to the left)
Work = (1/2) * (90 N/cm) * (-10.0 cm)^2
d) For x = -9.0 cm:
delta_x = -9.0 cm - 5.0 cm = -14.0 cm (negative because we're moving to the left)
Work = (1/2) * (90 N/cm) * (-14.0 cm)^2
Now, you can calculate the value of work using the above formulas for each case.