4. You are riding the Detonator at Worlds of Fun. It's a ride where you get accelerated straight up and down several times. Google it if that's a confusing description. a. How fast does the ride need to accelerate you upward at the beginning of the ride in order to make you feel twice as heavy as you normally do? (your apparent weight is twice your actual weight)

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### Physics of Amusement Park Rides: The Detonator

#### Problem 4

**Context:**
You are riding the Detonator at Worlds of Fun. It's a ride where you get accelerated straight up and down several times. If you are unfamiliar with this type of ride, you can look it up for clarity.

**Questions:**
a. How fast does the ride need to accelerate you upward at the beginning of the ride in order to make you feel twice as heavy as you normally do? (your apparent weight is twice your actual weight)

b. How fast does the ride need to drop when you are at the top so that you just barely leave your seat? Hint: What is the magnitude of the normal force when you barely lose contact with the seat?

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### Explanation:

1. **Understanding apparent weight:**
   - Apparent weight refers to the normal force exerted by a surface to support the weight of an object. 
   - On the Detonator ride, your apparent weight changes as the ride accelerates upwards or downwards. 

2. **Calculating acceleration for double apparent weight:**
   - When the ride accelerates upwards, the normal force increases.
   - To feel twice as heavy, the normal force should be twice your actual weight.
   - The relationship between acceleration and apparent weight can be given by Newton's second law.

3. **Conditions to barely leave the seat:**
   - When dropping, if the normal force becomes zero, you will feel weightless and start to lose contact with your seat.
   - This happens at the top of the drop when the acceleration due to the ride equals the gravitational acceleration.

These principles are key to solving the given physics problems regarding the dynamics of amusement park rides.
Transcribed Image Text:### Physics of Amusement Park Rides: The Detonator #### Problem 4 **Context:** You are riding the Detonator at Worlds of Fun. It's a ride where you get accelerated straight up and down several times. If you are unfamiliar with this type of ride, you can look it up for clarity. **Questions:** a. How fast does the ride need to accelerate you upward at the beginning of the ride in order to make you feel twice as heavy as you normally do? (your apparent weight is twice your actual weight) b. How fast does the ride need to drop when you are at the top so that you just barely leave your seat? Hint: What is the magnitude of the normal force when you barely lose contact with the seat? --- ### Explanation: 1. **Understanding apparent weight:** - Apparent weight refers to the normal force exerted by a surface to support the weight of an object. - On the Detonator ride, your apparent weight changes as the ride accelerates upwards or downwards. 2. **Calculating acceleration for double apparent weight:** - When the ride accelerates upwards, the normal force increases. - To feel twice as heavy, the normal force should be twice your actual weight. - The relationship between acceleration and apparent weight can be given by Newton's second law. 3. **Conditions to barely leave the seat:** - When dropping, if the normal force becomes zero, you will feel weightless and start to lose contact with your seat. - This happens at the top of the drop when the acceleration due to the ride equals the gravitational acceleration. These principles are key to solving the given physics problems regarding the dynamics of amusement park rides.
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