Explain 76 Question---Here is the extracted content from the image:
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**Q. 76**
**Question Stem:**
During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate of 1800 revolutions per minute about the vertical axis. The radius of the barrel is 36cm. What is the magnitude and direction of centripetal acceleration of the clothes which are located on the wall of the barrel?
**Options:**
The options are presented in a table format.
| | Magnitude | Direction |
|---|-----------------------|---------------------------------|
| A | 46.0 × 10⁶ ms⁻² | Towards the centre of the barrel |
| B | 46.0 × 10⁶ ms⁻² | Away from the centre of the barrel |
| C | 12.8 × 10³ ms⁻² | Towards the centre of the barrel |
| D | 12.8 × 10³ ms⁻² | Away from the centre of the barrel |
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**Q. 77**
**Question Stem:**
The maximum safe speed of a car rounding an unbanked corner is 16 m s⁻¹. When the road is dry. The maximum frictional force between the road surface and wheels of the car is halved when the road is wet. What is the maximum safe speed for the car to round the corner when the road is wet?
**Options:**
A. 4.0 m s⁻¹
B. 6.0 m s⁻¹
C. 8.0 m s⁻¹
D. 11 m s⁻¹
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Circular motion involves objects moving in circular paths. Key parameters include angular velocity omega, which equals 2 pi times frequency, linear velocity v equals omega times radius, and centripetal acceleration equals omega squared times radius, or v squared over radius. Centripetal acceleration always points toward the center of the circle.
Let's analyze the washing machine problem. We have a spin rate of 1800 revolutions per minute and a barrel radius of 36 centimeters. First, we convert units: 1800 rpm equals 30 Hz, giving us an angular velocity of 188.5 radians per second. The radius converts to 0.36 meters. The clothes experience centripetal acceleration pointing toward the center of the barrel.
Now let's calculate the centripetal acceleration step by step. First, we convert 1800 rpm to 188.5 radians per second. Then we apply the centripetal acceleration formula: a-c equals omega squared times r. Substituting our values: a-c equals 188.5 squared times 0.36, which gives us 35540 times 0.36, equals 12794 meters per second squared. This rounds to 12.8 times 10 to the third meters per second squared, pointing toward the center. The answer is option C.
Let's solve Question 76 about centripetal acceleration in a washing machine. We have clothes spinning at 1800 revolutions per minute in a barrel with radius 36 centimeters. We need to find the magnitude and direction of centripetal acceleration.
First, we convert 1800 RPM to radians per second. 1800 times 2 pi divided by 60 equals 188.5 radians per second. Then we calculate centripetal acceleration using omega squared times r. This gives us 188.5 squared times 0.36 meters, which equals approximately 12.8 times 10 to the 3rd meters per second squared. The direction is always toward the center of rotation.
Now let's solve Question 77 about a car rounding a corner. On a dry road, the maximum safe speed is 16 meters per second. When the road is wet, the maximum friction force is halved. We need to find the new maximum safe speed. The key is that maximum speed is proportional to the square root of friction force.
For circular motion, friction provides centripetal force equal to m v squared over r. On the dry road, this equals 256 m over r. When wet, friction is halved to 128 m over r. Setting this equal to m v wet squared over r, we get v wet squared equals 128. Taking the square root gives us 8 root 2, which is approximately 11.3 meters per second. The closest answer is 11 meters per second, option D.