A 200-kg cart is pushed slowly up an incline. How much work does the pushing force do in moving the cart up to a platform 1.5 m above the starting point if friction is negligible?
To find the work done by the pushing force in moving the cart up the incline, we need to know the force applied and the distance over which it acts.
The work done is equal to the force multiplied by the displacement in the direction of the force. In this case, the force is the pushing force exerted on the cart, and the displacement is the vertical distance the cart is lifted.
First, let's calculate the gravitational potential energy gained by the cart when it is lifted to a height of 1.5 m. The formula for gravitational potential energy is given by:
Gravitational Potential Energy = mass × acceleration due to gravity × height
Here, the mass of the cart is 200 kg, and the acceleration due to gravity is approximately 9.8 m/s². The height is given as 1.5 m.
Gravitational Potential Energy = 200 kg × 9.8 m/s² × 1.5 m
Gravitational Potential Energy = 2940 Joules
The work done by the pushing force is equal to the gravitational potential energy gained by the cart. Therefore, the work done by the pushing force in moving the cart up to the platform is 2940 Joules.