The work done on an object is given by the equation W = Fd cos θ, where F is the force applied, d is the distance over which the force is applied, and θ is the angle between the direction of the force and the direction of motion. 1. Pulling the boulder 2.00 m straight upwards at a constant speed: In this case, the force you apply is equal to the weight of the boulder (since you're lifting it straight up), and the distance over which you apply this force is 2.00 m. The angle θ is 0° (since the force and motion are in the same direction), so cos θ = 1. Therefore, the work done is W = F * 2.00 m * 1 = 2.00F. 2. Pulling the boulder along a 12.0° frictionless ramp at a constant speed until it reaches a height of 2.00 m: In this case, the force you apply is still equal to the weight of the boulder (since you're still lifting it against gravity), but the distance over which you apply this force is greater than 2.00 m (since the ramp is longer than the vertical height). The angle θ is 12.0° (since the force and motion are not in the same direction), so cos θ 2.00 m. Since d 2.00 m and cos 12.0°

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The work done on an object is given by the equation W = Fd cos θ, where F is the force applied, d is the distance over which the force is applied, and θ is the angle between the direction of the force and the direction of motion. 1. Pulling the boulder 2.00 m straight upwards at a constant speed: In this case, the force you apply is equal to the weight of the boulder (since you're lifting it straight up), and the distance over which you apply this force is 2.00 m. The angle θ is 0° (since the force and motion are in the same direction), so cos θ = 1. Therefore, the work done is W = F * 2.00 m * 1 = 2.00F. 2. Pulling the boulder along a 12.0° frictionless ramp at a constant speed until it reaches a height of 2.00 m: In this case, the force you apply is still equal to the weight of the boulder (since you're still lifting it against gravity), but the distance over which you apply this force is greater than 2.00 m (since the ramp is longer than the vertical height). The angle θ is 12.0° (since the force and motion are not in the same direction), so cos θ < 1. Therefore, the work done is W = F * d * cos 12.0°, where d > 2.00 m. Since d > 2.00 m and cos 12.0° < 1, the work done in this case is greater than 2.00F. Therefore, pulling the boulder along a 12.0° frictionless ramp at a constant speed until it reaches a height of 2.00 m requires more work.

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The work done on an object is given by the equation W = Fd cos θ, where F is the force applied, d is the distance over which the force is applied, and θ is the angle between the direction of the force and the direction of motion. 1. Pulling the boulder 2.00 m straight upwards at a constant speed: In this case, the force you apply is equal to the weight of the boulder (since you're lifting it straight up), and the distance over which you apply this force is 2.00 m. The angle θ is 0° (since the force and motion are in the same direction), so cos θ = 1. Therefore, the work done is W = F * 2.00 m * 1 = 2.00F. 2. Pulling the boulder along a 12.0° frictionless ramp at a constant speed until it reaches a height of 2.00 m: In this case, the force you apply is still equal to the weight of the boulder (since you're still lifting it against gravity), but the distance over which you apply this force is greater than 2.00 m (since the ramp is longer than the vertical height). The angle θ is 12.0° (since the force and motion are not in the same direction), so cos θ < 1. Therefore, the work done is W = F * d * cos 12.0°, where d > 2.00 m. Since d > 2.00 m and cos 12.0° < 1, the work done in this case is greater than 2.00F. Therefore, pulling the boulder along a 12.0° frictionless ramp at a constant speed until it reaches a height of 2.00 m requires more work.

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