A girl places a stick at an angle of 60.0° against a flat rock on a frozen pond. She pushes at an angle and moves the rock horizontally for 2.00 m across the pond at a velocity of 4.00 m/s and a power of 160.0 W. What force did she apply to the stick? How much work did she do? Your response should include all of your work. That way I can see what i don't understand! Thanks
power=work/time= force*distance/time=force*velocty
now solve for force in the horizontal direction.
Then, using the angle, find the force on the stick.
I will be happy to critique your work.
I am still lost! I understand the formula I just don't know what numbers to put where.
To solve this problem, we will use the concepts of work, power, and force.
Step 1: Determine the force applied to the stick.
We can use the equation for power to find the force applied.
Power (P) = Force (F) × Velocity (v)
Rearrange the equation to solve for force:
Force (F) = Power (P) / Velocity (v)
Given:
Power (P) = 160.0 W
Velocity (v) = 4.00 m/s
Substituting these values into the equation:
Force (F) = 160.0 W / 4.00 m/s
Force (F) = 40.0 N
Therefore, the force applied to the stick was 40.0 Newtons.
Step 2: Determine the work done.
To calculate the work done, we can use the equation:
Work (W) = Force (F) × Distance (d) × cos(θ)
Given:
Distance (d) = 2.00 m
Angle (θ) = 60.0°
First, convert the angle from degrees to radians:
θ (in radians) = 60.0° × (π radians / 180°)
θ (in radians) = 1.047 radians
Substituting the values into the equation:
Work (W) = 40.0 N × 2.00 m × cos(1.047)
Work (W) = 80.0 J × cos(1.047)
Work (W) ≈ 80.0 J × 0.5
Work (W) ≈ 40.0 J
Therefore, the girl did approximately 40.0 Joules of work.
To find the force applied to the stick, we can use the formula:
Force = Power / Velocity
Given:
Power (P) = 160.0 W
Velocity (v) = 4.00 m/s
Now, we can calculate the force:
Force = Power / Velocity
Force = 160.0 W / 4.00 m/s
Force = 40 N
So, the girl applied a force of 40 Newtons to the stick.
To find the work done, we can use the formula:
Work = Force × Distance × cos(θ)
Given:
Force (F) = 40 N
Distance (d) = 2.00 m
Angle (θ) = 60.0°
First, we need to convert the angle from degrees to radians:
Angle (θ in radians) = θ × π / 180
Angle (θ in radians) = 60.0° × π / 180
Angle (θ in radians) = π / 3
Now, we can calculate the work done:
Work = Force × Distance × cos(θ)
Work = 40 N × 2.00 m × cos(π / 3)
Work = 40 N × 2.00 m × 0.5
Work = 80 N·m
So, the girl did 80 Joules of work.