a loaded cart as a total mass of 227kg.if a 312-N force acting at angle of 30° to the ground is applied, how much work is done in moving the cart 15 meters?
Work = 312*cos30 * 15 = 4053 Joules.
To calculate the work done in moving the loaded cart, we need to use the formula:
Work = Force × Distance × cosθ
where:
Work is the work done (in joules),
Force is the force applied (in newtons),
Distance is the distance moved (in meters), and
θ (theta) is the angle between the force and the direction of motion.
Given:
Force = 312 N
Distance = 15 m
θ = 30°
Now, let's calculate the work done:
First, convert the angle from degrees to radians:
θ (in radians) = θ (in degrees) × π/180
θ (in radians) = 30° × π/180
θ (in radians) = 0.5236 radians
Next, calculate the work done using the formula:
Work = 312 N × 15 m × cos(0.5236 radians)
Now, use a calculator to find the cosine of 0.5236 radians:
cos(0.5236 radians) ≈ 0.866
Finally, substitute the values into the formula to calculate the work:
Work = 312 N × 15 m × 0.866
Now, multiply the values together to get the work done:
Work ≈ 4048.28 joules
Therefore, approximately 4048.28 joules of work is done in moving the cart 15 meters.