ojee a benz mechanic tries to remove an engine from a car by attaching a chain to it from a point directly overhead and then pulling sideways with horizontal force F.if the engine has mass 180 kg.what is the tension in the chain when it makes an angle of15degree with the vertical
1/2 force/tension= sin(15
tension= 1/2 force/sin15=90g/sin15
To calculate the tension in the chain, we can use the principles of trigonometry.
First, let's draw a diagram to visualize the scenario:
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In this diagram, the engine is represented by a rectangle. The chain is attached to the engine from a point directly overhead. The chain makes an angle of 15 degrees with the vertical.
Now let's analyze the forces acting on the engine:
1. The weight of the engine: This force acts vertically downward due to the gravitational force and can be calculated as follows:
weight = mass × acceleration due to gravity
weight = 180 kg × 9.8 m/s^2
weight = 1764 N (Newton) (downward)
2. The tension in the chain: This force acts horizontally and is the force being applied to pull the engine sideways. To find this force, we need to resolve the weight force into two components - one along the vertical direction and one along the horizontal direction.
The vertical component of the weight is:
weight_vertical = weight × sin(angle)
weight_vertical = 1764 N × sin(15°)
weight_vertical = 1764 N × 0.2588
weight_vertical = 456 N (upward)
The horizontal component of the weight is the same as the tension in the chain:
tension = weight × cos(angle)
tension = 1764 N × cos(15°)
tension = 1764 N × 0.9659
tension = 1704 N
Therefore, the tension in the chain when it makes an angle of 15 degrees with the vertical is approximately 1704 N.
To find the tension in the chain when it makes an angle of 15 degrees with the vertical, we can use the concept of resolved forces.
Here's how you can calculate it:
Step 1: Draw a diagram:
Start by drawing a diagram of the situation. Draw a vertical line to represent the chain, and mark the angle of 15 degrees from the vertical line.
Step 2: Resolve the forces:
Since the chain makes an angle with the vertical, we need to resolve the force into its vertical and horizontal components. The vertical component will oppose the weight of the engine, while the horizontal component will be responsible for pulling the engine sideways.
Step 3: Calculate the vertical component:
The vertical component of the force can be calculated using the formula:
Force_vertical = Force × cos(angle)
Substituting the given values:
Force_vertical = F × cos(15 degrees)
Step 4: Calculate the weight of the engine:
The weight of the engine can be calculated using the formula:
Weight = Mass × gravitational acceleration
Substituting the given values:
Weight = 180 kg × 9.8 m/s^2
Step 5: Equate the vertical components:
Since the vertical component of the force opposes the weight of the engine, we can equate them:
Force_vertical = Weight
Step 6: Solve for F (tension in the chain):
Rearrange the equation to solve for F:
F = Weight / cos(15 degrees)
Step 7: Calculate the tension in the chain:
Now, substitute the known values and calculate:
F = (180 kg × 9.8 m/s^2) / cos(15 degrees)
By performing the calculations, you can find the value of F, which represents the tension in the chain.