A child pulls a wagon by the handle along a flat sidewalk. She exerts a force of 80.0 N at an angle of 30.0 above the horizontal while she moves the wagon 12 m forward. The force of friction on the wagon is 34 N.
Calculate the mechanical work done by the child on the wagon
Calculate the total work done on the wagon
W = 831.38J
Ff = 34N
deltad = 12m
(b) W + (Ff x 12m)
= W + (-34N x 12m)
= 831.38J + (-408)
= 831.38J - 408
= 423.38J
Force/F= 80N
Angle=30 degrees
Distance/deltad=12m
Friction Force/Ff=34N
(a) W = Fcos(30)d
W = (80N)(cos30)(12m)
W = 831.38J
To calculate the mechanical work done by the child on the wagon, we need to calculate the component of the force in the direction of motion and multiply it by the distance the wagon was moved.
1. Calculate the component of the force in the direction of motion:
- The force exerted by the child can be split into two components: vertical and horizontal.
- The component in the horizontal direction is given by the formula: F_horizontal = F * cos(angle), where F is the force and angle is the angle above the horizontal.
- Plugging in the values, we get: F_horizontal = 80.0 N * cos(30.0°).
2. Calculate the work done by multiplying the horizontal component of force by the distance:
- The formula for work is: Work = Force * Distance.
- Plugging in the values, we get: Work = F_horizontal * distance.
To calculate the total work done on the wagon, we need to take into account the force of friction. Since the force of friction acts in the opposite direction to the motion of the wagon, the work done by the force of friction is negative.
3. Calculate the net work done on the wagon:
- The net work is given by the formula: Net Work = Work by applied force + Work by friction.
- Plugging in the values, we get: Net Work = Work - Work by friction.
Now, let's substitute the given values and calculate the answers.
Calculate the mechanical work done by the child on the wagon:
- The horizontal component of the force: F_horizontal = 80.0 N * cos(30.0°).
- The mechanical work done by the child: Work = F_horizontal * distance.
Calculate the total work done on the wagon:
- The work done by the applied force: Work = F_horizontal * distance.
- The work done by the force of friction: Work by friction = force of friction * distance.
- The net work done on the wagon: Net Work = Work - Work by friction.
Sure, let's calculate the mechanical work done by the child on the wagon.
The formula for calculating work is:
Work = Force * Distance * cos(θ)
Where:
Force = the magnitude of the force applied by the child (80.0 N)
Distance = the distance over which the force is applied (12 m)
θ = the angle between the force and the direction of motion (30.0°)
Using the formula, we can calculate the mechanical work:
Work = 80.0 N * 12 m * cos(30.0°)
Work = 960 N·m * cos(30.0°)
Work = 960 N·m * 0.866
Work ≈ 832.32 Joules
So, the mechanical work done by the child on the wagon is approximately 832.32 Joules.
Now, let's calculate the total work done on the wagon.
The total work done on an object is the sum of all the forces acting on it:
Total Work = Work done by the child - Work done by friction
The work done by friction is given as 34 N, and we already calculated the work done by the child as 832.32 Joules.
Total Work = 832.32 J - 34 J
Total Work ≈ 798.32 Joules
So, the total work done on the wagon is approximately 798.32 Joules.
Hope that helps!