a loaded cart has a total mass of 227kg. if a 312N force acting at an angle of 30 to the ground is applied, how much work is done by moving the cart 15m?
312 cos30*15 = ___ Joules
112
4052.99
W=F*d*cos(theta)
W=312*15*cos30
W=4052.998895
To calculate the work done by moving the cart, we need to multiply the force applied to the cart by the distance it is moved.
Work (W) = Force (F) * Distance (d) * cos(theta)
where theta is the angle between the force and the displacement.
In this case, the force applied is 312N, the distance moved is 15m, and the angle between the force and the ground is 30 degrees.
First, we calculate the horizontal component of the applied force using the given angle:
Horizontal Force (F_h) = Force (F) * cos(theta)
F_h = 312N * cos(30°)
F_h = 312N * √3/2
F_h ≈ 312N * 0.866
F_h ≈ 270.912N
Now, we can calculate the work done:
Work (W) = Horizontal Force (F_h) * Distance (d)
W = 270.912N * 15m
W ≈ 4063.68 Joules
Therefore, approximately 4063.68 Joules of work is done by moving the cart 15 meters.