How Much Work Is Done Against Gravity In Sliding A 500g Object Through 2m Up A Smooth Plane That Is Inclined 30degree To The Horizontal(g=9.8)
Its sin not cos
W=F×scos#
=ma×s cos#
=0.5kg×9.8×2×cos30°
=9.8×0.5
=9.8×1/2
=9.8/2
=4.9J
To find the work done against gravity in sliding a 500g object through 2m up a smooth plane inclined at 30 degrees to the horizontal, we need to consider the force of gravity acting on the object and the distance it moves.
Step 1: Calculate the weight of the object.
The weight of the object is given by the formula:
Weight = mass x acceleration due to gravity
Weight = 0.5kg x 9.8m/s^2
Weight = 4.9N
Step 2: Calculate the vertical distance the object moves.
The vertical distance is given by the formula:
Vertical distance = horizontal distance x sin(angle of inclination)
Vertical distance = 2m x sin(30 degrees)
Vertical distance = 2m x 0.5
Vertical distance = 1m
Step 3: Calculate the work done against gravity.
The work done against gravity is given by the formula:
Work = force x distance
Work = weight x vertical distance
Work = 4.9N x 1m
Work = 4.9 Joules
Therefore, the work done against gravity in sliding a 500g object through 2m up a smooth plane inclined at 30 degrees to the horizontal is 4.9 Joules.
To calculate the amount of work done against gravity, you need to determine the vertical displacement of the object and the force acting against gravity. Here's how you can find the answer step by step:
1. Calculate the vertical displacement: In this case, the object is being moved vertically upwards by 2m. Therefore, the vertical displacement is +2m.
2. Calculate the force against gravity: The force against gravity is equal to the weight of the object. The weight (W) is given by the formula W = m * g, where m is the mass of the object and g is the acceleration due to gravity. In this case, the mass of the object is 500g, which is equal to 0.5kg, and the acceleration due to gravity is 9.8 m/s². Therefore, the force against gravity is calculated as follows:
W = m * g
W = 0.5kg * 9.8 m/s²
W = 4.9 N
3. Calculate the work done against gravity: The work done against gravity is given by the formula W = F * d * cos(theta), where F is the force against gravity, d is the displacement, and theta is the angle between the force vector and the displacement vector. In this case, the force against gravity is 4.9 N, the displacement is 2 m, and the angle theta is 30 degrees. However, since the displacement is in the same direction as the force, the angle between them is 0 degrees. Therefore, cos(theta) = cos(0) = 1, and the formula becomes:
W = F * d * cos(theta)
W = 4.9 N * 2 m * 1
W = 9.8 J
Therefore, the work done against gravity in sliding a 500g object through 2m up a smooth plane inclined 30 degrees to the horizontal is 9.8 Joules.