a loaded cart as a total mass of 227kg.if a 312-N force acting at angle of 30° to the ground is applied, how much work is done in moving the cart 15 meters?
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To find the work done in moving the cart, we need to calculate the magnitude of the force parallel to the direction of motion and multiply it by the distance moved.
1. Calculate the component of the force parallel to the ground:
- The force acting at an angle of 30° to the ground can be divided into two perpendicular components: one parallel to the ground and one perpendicular to the ground.
- The component parallel to the ground can be found using the formula: F_parallel = F * cos(θ), where F is the magnitude of the force and θ is the angle between the force and the ground.
- Substitute the values: F_parallel = 312 N * cos(30°)
2. Calculate the work done:
- The work done is given by the formula: Work = Force * Distance, where Force is the component of the force parallel to the ground and Distance is the distance moved.
- Substitute the values: Work = F_parallel * Distance
Now let's do the calculations:
1. Calculate the component of the force parallel to the ground:
F_parallel = 312 N * cos(30°)
= 312 N * √3/2
≈ 270.4 N
2. Calculate the work done:
Work = F_parallel * Distance
= 270.4 N * 15 m
≈ 4056 J
Therefore, the work done in moving the cart 15 meters is approximately 4056 joules (J).