3. A hand truck is used to move an R-134a cylinder. Knowing that the combined weight of the truck and cylinder is 180 lbs acting at the center of gravity G, determine the vertical force A which must be applied to the handle to maintain the cylinder at this 60° angle, and also the corresponding reaction at each of the two wheels. A 60° 19 in 26 in 9 in
3. A hand truck is used to move an R-134a cylinder. Knowing that the combined weight of the truck and cylinder is 180 lbs acting at the center of gravity G, determine the vertical force A which must be applied to the handle to maintain the cylinder at this 60° angle, and also the corresponding reaction at each of the two wheels. A 60° 19 in 26 in 9 in
International Edition---engineering Mechanics: Statics, 4th Edition
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ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter10: Virtual Work And Potential Energy
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Problem 10.62P: The bar ABC is supported by three identical, ideal springs. Note that the springs are always...
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Answer should be : Force on the handle A= 49.32 lb (up) ; force on each wheel B= 65.lb
![### Example Problem: Hand Truck for an R-134a Cylinder
#### Problem Statement:
A hand truck is used to move an R-134a cylinder. Knowing that the combined weight of the truck and the cylinder is 180 lbs acting at the center of gravity \( G \), determine the vertical force \( A \) that must be applied to the handle to maintain the cylinder at a 60° angle. Additionally, find the corresponding reaction at each of the two wheels.
#### Diagram Explanation:
The provided diagram shows a hand truck with the following annotations:
- **Angle**: The hand truck is tilted at an angle of 60° with respect to the horizontal surface.
- **Vertical Force \( A \)**: An upward vertical force \( A \) is applied at the handle of the truck in order to maintain the cylinder at the specified angle.
- **Weight**: The combined weight of the truck and cylinder is given as 180 lbs, which acts downward at the center of gravity \( G \).
- **Distances**:
- From the wheel to the point where the center of gravity \( G \) is located along the length of the truck is 26 inches.
- From the wheel to the handle is 19 inches, measured horizontally.
- The height of the wheels is 9 inches from the ground.
#### Step-by-Step Solution:
1. **Identify the forces and their points of application**:
- Weight \( W \) = 180 lbs, acting vertically downward at \( G \).
- The vertical force \( A \), acting at the handle.
- Reactions at the wheels, which can be denoted as \( R_1 \) and \( R_2 \) for each side.
2. **Apply the equilibrium conditions**:
- **Sum of vertical forces**: To ensure vertical equilibrium, the sum of all vertical forces must be zero.
\[
A - W + R_1 + R_2 = 0
\]
- **Sum of moments about the wheels**: To maintain rotational equilibrium, the sum of the moments about the point where the wheels touch the ground must be zero.
3. **Calculate the necessary vertical force and reactions**:
- Use trigonometry and principles of static equilibrium to solve for the unknown forces.
By following these steps and applying the equilibrium equations, we can determine the specific values for the force \( A \) and the reactions \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff12ec146-5781-453b-8388-2e7cc9921f6c%2F0fbaa0c8-ec8a-41e3-9df5-9a4baa8e9d9e%2F6nh42rf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem: Hand Truck for an R-134a Cylinder
#### Problem Statement:
A hand truck is used to move an R-134a cylinder. Knowing that the combined weight of the truck and the cylinder is 180 lbs acting at the center of gravity \( G \), determine the vertical force \( A \) that must be applied to the handle to maintain the cylinder at a 60° angle. Additionally, find the corresponding reaction at each of the two wheels.
#### Diagram Explanation:
The provided diagram shows a hand truck with the following annotations:
- **Angle**: The hand truck is tilted at an angle of 60° with respect to the horizontal surface.
- **Vertical Force \( A \)**: An upward vertical force \( A \) is applied at the handle of the truck in order to maintain the cylinder at the specified angle.
- **Weight**: The combined weight of the truck and cylinder is given as 180 lbs, which acts downward at the center of gravity \( G \).
- **Distances**:
- From the wheel to the point where the center of gravity \( G \) is located along the length of the truck is 26 inches.
- From the wheel to the handle is 19 inches, measured horizontally.
- The height of the wheels is 9 inches from the ground.
#### Step-by-Step Solution:
1. **Identify the forces and their points of application**:
- Weight \( W \) = 180 lbs, acting vertically downward at \( G \).
- The vertical force \( A \), acting at the handle.
- Reactions at the wheels, which can be denoted as \( R_1 \) and \( R_2 \) for each side.
2. **Apply the equilibrium conditions**:
- **Sum of vertical forces**: To ensure vertical equilibrium, the sum of all vertical forces must be zero.
\[
A - W + R_1 + R_2 = 0
\]
- **Sum of moments about the wheels**: To maintain rotational equilibrium, the sum of the moments about the point where the wheels touch the ground must be zero.
3. **Calculate the necessary vertical force and reactions**:
- Use trigonometry and principles of static equilibrium to solve for the unknown forces.
By following these steps and applying the equilibrium equations, we can determine the specific values for the force \( A \) and the reactions \(
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