As part of a training schedule a weightlifter pushes a heavy metal block
along the floor. The lifter applies a force of 850 N downwards on the block
at an angle of 65° to the vertical (25° to the horizontal). The weightlifter
pushes the block forwards 4 m in 1.6 s. Calculate the power output of the
weightlifter when moving the block 4 m forwards. [10 marks]
F = 850N @ 25 Deg.
Fx = 850*cos25 = 770.4 N. = hor. Force.
Fy = 850*sin25 = 359.2 N. = Ver. force.
P = Fx*V = Fx * (d/t).
P=770.4 * (4/1.6) = 1926 J/s=1926 J/s =
1926 Watts.
Well, let me calculate the answer for you, but before I do, let me tell you a joke. Why don't scientists trust atoms? Because they make up everything!
Now, back to business. To calculate the power output of the weightlifter, we need to know the work done first. We can use the work formula:
Work = Force x Distance x cos(angle)
In this case, the force is 850 N, the distance is 4 m, and the angle is 25°. So now I'll crunch the numbers for you:
Work = 850 N x 4 m x cos(25°)
And the answer is... *drumroll*... Work = 3,727.014 J (approximately).
Now we can calculate the power using the formula:
Power = Work / Time
Since the weightlifter did the work in 1.6 s, we can find the power:
Power = 3,727.014 J / 1.6 s
And the final answer is... *more drumroll*... Power = 2,329.384 W (approximately).
So, the power output of the weightlifter when moving the block 4 m forwards is approximately 2,329.384 watts. That's quite powerful!
To calculate the power output of the weightlifter, we need to use the formula:
Power = Work / Time
Step 1: Calculate the work done by the weightlifter.
The work done can be calculated using the formula:
Work = Force x Distance x cos(θ)
Given:
Force (F) = 850 N
Distance (d) = 4 m
θ = 65° (angle to the vertical, or 25° to the horizontal)
Using the formula, we can calculate the work done:
Work = 850 N x 4 m x cos(65°)
Step 2: Convert the angle from degrees to radians.
To use the cosine function in the formula, we need to convert the angle from degrees to radians.
θ (in radians) = θ (in degrees) x π/180
θ (in radians) = 65° x π/180
Step 3: Calculate the work done.
Work = 850 N x 4 m x cos(65° x π/180)
Step 4: Calculate the power output.
Given:
Time (t) = 1.6 s
Using the formula, we can calculate the power output:
Power = Work / Time
Power = (850 N x 4 m x cos(65° x π/180)) / 1.6 s
Calculating this expression will give us the power output of the weightlifter.
To calculate the power output of the weightlifter, we will use the formula:
Power = Work / Time
First, let's calculate the work done by the weightlifter on the block.
Work is equal to the force applied in the direction of motion, multiplied by the distance covered. In this case, the force applied by the weightlifter is not directly in the direction of motion, so we need to calculate the component of the force in the direction of motion.
1. Calculate the vertical component of the force:
Vertical component = Force * sin(65°)
Vertical component = 850 N * sin(65°)
2. Calculate the horizontal component of the force:
Horizontal component = Force * cos(65°)
Horizontal component = 850 N * cos(65°)
To find the work done by the weightlifter, we multiply the horizontal component of the force by the distance covered.
Work = Horizontal component * distance
Work = (850 N * cos(65°)) * 4 m
Now, we have the work done by the weightlifter. Next, we need to calculate the power by dividing that work by the time taken.
Power = Work / Time
Power = ((850 N * cos(65°)) * 4 m) / 1.6 s
Now, you can calculate the power output of the weightlifter.