Balance the following equations:
1 answer:
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Answer: Total work done on the block is 3670.5 Joules.
Step by step:
Work done:
With F the force, d the displacement, and theta the angle of action (which is 0 since the block is pushed along the direction of displacement, and cos 0 = 1)
Given:
F = 75 N
m = 31.8 kg
Final velocity
In order to calculate the Work we need to determine the displacement, or distance the block travels. We can use the information about F and m to first figure out the acceleration:
Now we can determine the displacement from the following formula:
Here, the initial displacement is 0 and initial velocity is also 0 (at rest):
Now we still have "t" as unknown. But we are given one more bit of information from which this can be determined:
(using vf as final velocity, and tf as final time)
So it takes about 6.44 seconds for the block to move. This allows us to finally calculate the displacement:
and the corresponding work:
It is calculated that a)The angular velocity of the wheel is 272.13 rad/s,
b)On the edge of the grinding wheel, the linear speed is 47.62 m/s,
and c) On the edge of the grinding wheel, the acceleration is 12958.08 m/s².
Calculation of angular velocity, linear speed & acceleration:
Provided that,
the diameter of the wheel = 0.35 m
So, the radius, r = 0.35/2 = 0.175 m
As 1 revolution = 2π rad
(a)the angular velocity, ω = 2600 rpm = rad/s
⇒ω = 272.13 rad/s
So, the angular velocity is 272.13 rad/s.
(b)The linear speed, v = r * ω
⇒v = 0.175 * 272.13
⇒v= 47.62 m/s
(c)The angular acceleration,
⇒ = 12958.08 m/s²
Learn more about angular velocity here:
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