While curling, you push a rock for 2.00 m and release it when it has a speed of 1.90 m/s. It continues to slide at constant speed for 0.700 s and then hits a rough patch of ice. It finally comes to rest 8.30 m from where it was released. What was the curling rock's magnitude of acceleration after it hit the patch of rough ice?
vf^2=vi^2+2ad or
0=1.9^2 + 2a*8.3 solve for acceleration a.
initial speed = 1.90 m/s at release
slides at that speed for 0.7 s so goes 1.33 m
slows at constant acceleration
stops in 8.30 - 1.33 = 6.97 meters
average speed during stop = 1.90/2 = 3.485 m/s
so time to stop = 6.97 /3.485 = 2 seconds on the rough ice
a = change in speed / time = 1.90/2 = 0.95 m/s^2
slides after release at 1.9 until it hits the rough spot so only brakes for about 7 meters
To find the magnitude of acceleration of the curling rock after it hits the rough patch of ice, we need to use the equation of motion, specifically the equation that relates displacement, initial velocity, time, and acceleration:
s = ut + (1/2)at^2,
where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Let's break down the problem step by step:
Step 1: Find the initial velocity (u):
The initial velocity of the rock is 1.90 m/s, as given in the problem statement.
Step 2: Find the time (t):
The rock continues to slide at constant speed for 0.700 s, as mentioned in the problem.
Step 3: Find the displacement (s):
The rock comes to rest 8.30 m from where it was released.
Step 4: Find the acceleration (a):
We need to calculate the acceleration after the rock hits the rough patch of ice.
To find the acceleration, we can rearrange the equation of motion:
a = 2(s - ut) / t^2.
Substituting the known values, we get:
a = 2(8.30 m - (1.90 m/s * 0.700 s)) / (0.700 s)^2.
Simplifying further:
a = 2 * (8.30 m - 1.33 m) / (0.49 s^2).
a = 2 * 6.97 m / 0.2401 s^2.
a = 13.94 m / 0.2401 s^2.
a ≈ 58.1 m/s^2.
Therefore, the magnitude of acceleration of the curling rock after hitting the rough patch of ice is approximately 58.1 m/s^2.