Question

STEP 1 Force: Just after releasing the block, calculate the force exerted on the block by the spring, the force exerted on the block by the Earth, and the net force: spring,r# 2.64 Earthy-6769 net.y - 1.96 0.676N 1.96 N Momentum update: Just after releasing the block, the momentum of the block is zero. Approximate the average net force during the next timel by the force you just calculated. At t0.07 seconds, what will the new momentum and velocity of the block be? Py-1372 Vy1.98 kg m/s m/s Position update: Initially the bottom of the block is at y 0.12 m. Approximating the average velocity in the first time interval by the final velocity, what will be the new position of the bottom of the block at time t-0.07 seconds? r= .2592 STEP 2 Force: At the new position, calculate the force exerted on the block by the spring, the force exerted on the block by the Earth, and the net force spring.y FEarth,y Momentum update: Approximate the average net force during the next time interval by the force you just calculated. At time t = 2 x 0.07 = 0.14 seconds, what will the new momentum and velocity of the block be? kg m/s mys Position update: Approximating the average velocity in the second time interval by the final velocity, what will be the new position of the bottom of the block at time t-2 × 0.07-0.14 seconds? STEP 3 Force: At the new position, calculate the force exerted onthe block by the spring, the force exerted on the block by the Earth, and the net force: spring.y Earth.y Momentum update: Approximate the average net force during the next time interval by the force you just calculated. At time t-3 x 0.07-0.21 seconds, what will the new momentum and velocity of the block be? Py kg m/s mys Position update: Approximating the average velocity in the third time interval by the final velocity what will be the new position of the bottom of the block at time t = 3 x 0.07 0.21 seconds?

Answer 1

Step 2:

force exerted by the spring =spring constant*compression

=12*(0.34 - 0.2592) = 0.9696 N

force is directed vertically upwards.

part 2:

force by earth = weight of the block = mass*g

= 0.069*9.8 = 0.676 N

force is directed vertically downward.

part 3:

net force is in vertically upward direction.

net force = 0.9696 - 0.676 = 0.293 N

part 4:

change in momentum = force*time duration

py - 0.1372 = 0.293*0.07

py = 0.1577 kg.m/s

part 5:

velocity at t = 0.07 s

v = py/mass =0.1577/0.069 = 2.28 m/s

part 6:

new position at t=0.07 seconds

y = initial position+ velocity*time

y = 0.2592 + 2.28*0.07 = 0.4192 m

Step 3:

force exerted by the spring =spring constant*compression

=12*(0.34 - 0.4192) = -0.9504 N

force is directed vertically downward.

part 2:

force by earth = weight of the block = mass*g

=0.069*9.8 = 0.676 N

force is directed vertically downward.

part 3:

net force is in vertically upward direction.

net force = -0.9504 -0.676 = -1.626 N

part 4:

change in momentum = force*time duration

py - 0.1577 = -1.626*0.07

py = 0.0438 kg.m/s

part 5:

velocity at t=0.07 seconds

v = py/mass =0.0438/0.069 = 0.6347 m/s

part 6:

new position at t=0.04 seconds

y = initial position+ velocity*time

y =0.4192 +0.6347*0.07 = 0.4636 m