4) You are testing a new tire material with exceptional friction properties. You are testing it by driving around a circular track with radius R. The friction is providing the centripetal accelerati ac; your new tires can provide a maximum ac,max. You are driving on the track, for parts a.-c. y are driving with constant speed v₁; for d. and e. you are accelerating with a constant tangential acceleration at. a. Driving with vt, what is your centripetal acceleration; and what is your angular velocity? b. What are the maximum safe tangential and angular speed? At this speed, how long do it take to drive q full circles? c. Now you are accelerating with at from rest. What is your angular acceleration? What a your tangential and angular speeds after one full circle? d. Where on the circle are you reaching ac,max? e. If R = 50 m, a, = 5 ms2, ac,max = 25 ms2, what is the numerical answer to d.?
4) You are testing a new tire material with exceptional friction properties. You are testing it by driving around a circular track with radius R. The friction is providing the centripetal accelerati ac; your new tires can provide a maximum ac,max. You are driving on the track, for parts a.-c. y are driving with constant speed v₁; for d. and e. you are accelerating with a constant tangential acceleration at. a. Driving with vt, what is your centripetal acceleration; and what is your angular velocity? b. What are the maximum safe tangential and angular speed? At this speed, how long do it take to drive q full circles? c. Now you are accelerating with at from rest. What is your angular acceleration? What a your tangential and angular speeds after one full circle? d. Where on the circle are you reaching ac,max? e. If R = 50 m, a, = 5 ms2, ac,max = 25 ms2, what is the numerical answer to d.?
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Transcribed Image Text:**Title: Tire Material Testing on a Circular Track**
**Context:**
You are testing a new tire material with exceptional friction properties. The test involves driving around a circular track with radius \( R \). Friction provides the centripetal acceleration \( a_c \); the new tires can supply a maximum of \( a_{c,\text{max}} \). The test comprises different scenarios:
**Scenarios:**
a. **Constant Speed \( v_t \):**
- Determine the centripetal acceleration and angular velocity.
b. **Maximum Safe Speeds:**
- Calculate the maximum safe tangential and angular speeds.
- Estimate the time required to drive \( q \) full circles at this speed.
c. **Acceleration from Rest:**
- Starting with tangential acceleration \( a_t \), find the angular acceleration.
- Assess tangential and angular speeds after one full circle.
d. **Reaching Maximum Acceleration:**
- Identify the point on the circle where \( a_c = a_{c,\text{max}} \).
e. **Numerical Analysis:**
- Given \( R = 50 \, \text{m}, a_t = 5 \, \text{m/s}^2, a_{c,\text{max}} = 25 \, \text{m/s}^2 \), calculate the numerical answer for scenario d.
**Objective:**
To determine the performance limits and dynamics of new tire materials under varying conditions of speed and acceleration on a controlled circular track.
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We are given a tire in circular motion. The centripetal force is not a force in itself. This force is provided by some other external force. This centripetal force is provided by friction here. We find centripetal acceleration and velocity both angular and linear.
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