Question

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? y = 1. m

Answer 1

The new position of the bottom of the block at time t = 0.07 seconds is 1 m.

Step-by-step explanation:

To find the new position of the bottom of the block at time t = 0.07 seconds, we can use the concept of average velocity. The average velocity is given by the change in position divided by the change in time. In this case, if we approximate the average velocity in the first time interval by the final velocity, we can say that the change in position is equal to the average velocity multiplied by the change in time. The new position can then be calculated by adding this change in position to the initial position.

Given that the initial position of the bottom of the block is at y = 0.12 m and the final velocity is approximated to be y = 1 m, we can calculate the change in position as:

Change in position = (Final velocity - Average velocity) * Change in time = (1 m - 0.12 m) * (0.07 s - 0 s) = 0.88 m

Therefore, the new position of the bottom of the block at time t = 0.07 seconds is y = 0.12 m + 0.88 m = 1 m.

Answer 2

The new position is 0.1865 m

Step-by-step explanation:

As the context of the data is not available, thus following data is utilized from the question as attached above

x_relax=0.32 m

x_stiff=0.13 m

spring stiffness k=9 N/m

mass of block =0.073 kg

t=0.07 s

Velocity of the block is to be estimated thus

Force due to compression in spring is given as

F_s=k Δx

F_s=9(0.32-0.13)

F_s=1.71 N

Force on the block is given as

F_m=mg

F_m=0.073 x 9.8

F_m=0.71 N

Net Force

F=F_s-F_m

F=1.71-0.71 N

F=1 N

As Ft=Δp

So

Δp=1x0.07=0.07 kgm/s

Δp=p_final-p_initial

0.07=p_final-0

p_final=0.07 kgm/s

p_final=m*v_f

v_f=(p_final)/(m)

v_f=0.07/0.073

v_f=0.95 m/s

So now the velocity of the block is 0.95 m/s

time is 0.07 s

y_new=y_initial+y_travel

y_new=0.12+(0.95 x 0.07)

y_new=0.12+0.065

y_new=0.1865 m

So the new position is 0.1865 m