Linear and Angular Motion Help

[JohnP60]

Homework Statement

Need a bit off help with these questions would appreciate some help.

Homework Equations

1. An accelerating vehicle crosses a datum with a velocity of 20m/s and then covers a distance of 2.5km in 50s. Calculate the acceleration, and the velocity reached after it has traveled 2.5km.

2. If a rotor is rotating at 2000 rev/min accelerates to 3000 rev/min in 6 seconds calculate its acceleration and angle turned through.

3. Calculate the velocity of a belt in a belt drive system where the pulley is 82.3cm diameter and rotates at:
a) 1750 rev/min
b) 40 rev/s

The Attempt at a Solution

1. a=v-u / t
20/50 = 0.4m/s^2

v=u+at
20 + 0.4 x 50 = 40m/s

2. 314.16 - 209.43 / 6 = 17.5 rad/s^2

w= wo t + 1/2 a t^2
1256.58 + 315
= 1571.58 rad

3. Unsure how to do this one

Thanks

 

[mfb]

1. a=v-u / t
20/50 = 0.4m/s^2

This assumes the velocity changes by 20m/s in 50 seconds. You don't know if that is true.

v=u+at
20 + 0.4 x 50 = 40m/s

Simple cross-check: if the vehicle drives with a speed between 20m/s and 40m/s, in 50s it cannot go further than 40m/s*50s = 2km. Certainly not 2.5km.
Checks like those are useful to see if your answer can make sense.

314.16 - 209.43 / 6 = 17.5 rad/s^2

There are missing brackets, but this problem will vanish with proper fractions on paper.
I can confirm your answer.

3. The pulley is a circle, the belt is moving at the outer edge with the same speed as this outer edge.

 

[JohnP60]

Unsure what you mean with Q1. Am i using wrong formulas?

had a go at 3.

a)V=Rw
0.41x183.26
=75.14m/s

b)V=Rw
0.41x251.33
=103.04m/s

 

[mfb]

Unsure what you mean with Q1. Am i using wrong formulas?

Yes.

3 looks good.

As a general remark, it is easier to understand what you are doing if you start with a formula, and with the values given in the problem statement.

 

[HalfLostAndSearching]

for reaching out for help with your homework questions on linear and angular motion. I'd be happy to assist you in solving these problems.

1. For the first question, you are given the initial velocity (u = 20m/s), final velocity (v = unknown), and time (t = 50s). Using the equation a = (v-u)/t, we can rearrange it to solve for v. So, v = u + at. Plugging in the values, we get v = 20 + 0.4 x 50 = 40m/s. This is the velocity reached after traveling 2.5km.

2. In the second question, you are given the initial angular velocity (wo = 2000 rev/min), final angular velocity (w = 3000 rev/min), and time (t = 6s). We can use the equation a = (w-w0)/t to solve for acceleration. So, a = (3000-2000)/6 = 167 rad/s^2. To find the angle turned through, we can use the equation w = wo + at. Plugging in the values, we get w = 2000 + 167 x 6 = 2998 rad/min.

3. For the third question, we need to use the formula v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the pulley. The radius is half the diameter, so r = 41.15cm = 0.412m.

a) For the first part, we are given the angular velocity (ω = 1750 rev/min). We need to convert this to radians per second, so ω = 1750 x 2π/60 = 183.33 rad/s. Plugging this into the formula, we get v = 183.33 x 0.412 = 75.56m/s.

b) For the second part, we are given the angular velocity (ω = 40 rev/s). Plugging this into the formula, we get v = 40 x 0.412 = 16.48m/s.

I hope this helps you with your homework questions. Remember to always check your units and use the correct formulas for each problem. Good luck!