If you pull a 10-kilogram cart along the ground for 5 meters using 2 Newtons of force,how high will it go before it stops?
To determine the height the cart will go before it stops, we need to consider the work done and the potential energy gained.
First, let's calculate the work done using the formula:
Work (W) = Force (F) * Distance (d) * cos(angle)
Since the force is applied horizontally, the angle between the force and the displacement is 0 degrees, and cos(0) = 1. Therefore, we can simplify the formula to:
Work (W) = Force (F) * Distance (d)
Substituting the given values:
W = 2 Newtons * 5 meters
W = 10 Joules
Now, we can calculate the potential energy gained by the cart using the equation:
Potential energy (PE) = Mass (m) * Gravity (g) * Height (h)
As the cart stops, all the work done will be converted into potential energy. Thus, we can equate the work done to the potential energy gained:
Potential energy (PE) = Work (W)
mgh = 10 Joules
Since the mass (m) is given as 10 kilograms and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we can solve for the height (h):
(10 kg) * (9.8 m/s^2) * h = 10 Joules
simplifying further,
h = 10 Joules / (98 kg m/s^2)
h = 0.102 meters
Therefore, the cart will go approximately 0.102 meters (or 10.2 centimeters) high before it stops.