A horse pulls a cart with a force of 145 newtons at an angle of 30 degrees above the horizontal and moves along at a speed of 2.5 m/s. How much work to the nearest kJ does the force do in 6 minutes?
d = 2.5m/s * 6min*60s/min = 900 m.
Work = F*d = 145cos30 * 900 = 443,856 J.
= 444 kJ.
Vector A has a magnitude of 5.00units,and B has a magnitude of 9.00units.The two vectors make an angle of 50.0degrees with each other .Find A.B.
To calculate the work done by the force, we need to know the distance traveled by the horse and cart. Since the speed is given in m/s, we can use the formula:
Distance = Speed × Time
In this case, the time is given as 6 minutes, so we need to convert it to seconds:
Time = 6 minutes × 60 seconds/minute = 360 seconds
Now, let's calculate the distance traveled:
Distance = Speed × Time = 2.5 m/s × 360 s = 900 meters
Now, we can calculate the work done using the formula:
Work = Force × Distance × cos(θ)
where θ is the angle between the force and the direction of motion. In this case, the angle is given as 30 degrees:
Work = 145 N × 900 m × cos(30°)
To calculate the cosine of 30 degrees, we can use a calculator or a math function:
cos(30°) ≈ 0.866
Now we can plug in the values:
Work = 145 N × 900 m × 0.866 ≈ 110,610 joules
To convert joules to kilojoules, we divide by 1000:
Work ≈ 110,610 joules / 1000 = 110.61 kilojoules
Therefore, the work done by the force is approximately 110.61 kilojoules.
To calculate the work done by the force, we need to use the formula:
Work = Force × Distance × cos(angle)
First, let's convert the time from minutes to seconds since the other units are in SI (International System) units. There are 60 seconds in a minute, so 6 minutes is equal to 6 × 60 = 360 seconds.
We also need to find the distance traveled by the horse in 360 seconds. To do that, we can use the formula:
Distance = Speed × Time
Given that the speed is 2.5 m/s and the time is 360 seconds, the distance is:
Distance = 2.5 m/s × 360 s = 900 meters
Now we can calculate the work done:
Work = 145 N × 900 m × cos(30 degrees)
The cos(30 degrees) can be calculated using a calculator or by using the value of √3/2 for cos(30 degrees). Substituting this value:
Work = 145 N × 900 m × (√3/2)
Now we can simplify the calculation further:
Work = 130,500 N·m × (√3/2)
Finally, to convert the unit N·m to kilojoules (kJ), we divide by 1000:
Work = (130,500 N·m × (√3/2)) / 1000
Therefore, the work done by the force of the horse pulling the cart in 6 minutes is approximately:
Work = 190.19 kJ (rounded to the nearest kJ)