What tension is needed to make a cart with mass 24 kg go up an incline at a constant velocity?

To determine the tension necessary to move a cart up an incline at a constant velocity, we need to consider the forces acting on the cart. When the cart is moving at a constant velocity, the net force acting on it must be zero, meaning that all forces are balanced.

The primary forces to consider are the component of gravitational force acting down the incline and the tension in the rope pulling the cart upward. The gravitational force acting on the cart can be calculated using the equation:

[ F_g = mg ]

where ( m ) is the mass of the cart and ( g ) is the acceleration due to gravity, approximately ( 9.81 , \text{m/s}^2 ). For a cart with a mass of 24 kg:

[ F_g = 24 , \text{kg} \times 9.81 , \text{m/s}^2 = 235.44 , \text{N} ]

This gravitational force acts vertically downward. When considering an incline, the force acting along the incline (the downhill component of the gravitational force) can be found by multiplying the gravitational force by the sine of the angle of the incline (( \theta )). This component can