How much work is needed to push a 1250kg cart 11.5m up at 13.5° incline at constant velocity?
work = mgh = 1250*9.81 * 11.5 sin13.5°
To calculate the amount of work needed to push a cart up an incline at constant velocity, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Force is the component of the force being applied parallel to the incline.
- Distance is the displacement along the incline.
- θ is the angle of inclination.
In this case, the force required to push the cart up the incline at constant velocity is equal to the force of gravity acting on the cart, which can be calculated as:
Force = mass × acceleration due to gravity
The mass of the cart is given as 1250 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Force = 1250 kg × 9.8 m/s^2 = 12250 N
Since the cart is moving at a constant velocity, the force applied parallel to the incline is equal in magnitude and opposite in direction to the force of friction, given by:
Force of friction = Force = 12250 N
Next, we need to calculate the distance the cart is being pushed up the incline. In this case, the given distance is 11.5 m.
Distance = 11.5 m
The angle of inclination is 13.5°.
θ = 13.5°
Finally, we can calculate the work needed to push the cart up the incline using the formula:
Work = Force × Distance × cos(θ)
Work = 12250 N × 11.5 m × cos(13.5°)
Calculating this expression will give us the work needed to push the cart up the incline at constant velocity.
To find the amount of work needed to push a cart up an incline at constant velocity, we need to calculate the gravitational potential energy gained by the cart. The work done is equal to the change in potential energy.
First, let's find the height the cart is lifted:
h = sin(13.5°) * 11.5m
h = 2.631m
Next, we can calculate the change in gravitational potential energy using the formula:
ΔPE = m * g * h
Where:
ΔPE = change in potential energy
m = mass of the cart (1250 kg)
g = acceleration due to gravity (approx. 9.8 m/s^2)
h = height (2.631 m)
Plugging in the values:
ΔPE = 1250 kg * 9.8 m/s^2 * 2.631 m
ΔPE ≈ 32,136.65 Joules
Therefore, the amount of work needed to push the 1250 kg cart up the incline at constant velocity is approximately 32,136.65 Joules.