A 45 kg car is pulled at a constant speed across a rough horizontal road by a rope at an angle of 29.5o above horizontal. How much work is done by the rope on the car to move 12 m if the tension in the rope is 216 N?
The work done by the rope on the car is given by the equation:
W = Fd cosθ
where W is the work done (in joules), F is the force exerted by the rope (in newtons), d is the distance moved (in meters), and θ is the angle between the force and the direction of motion (in degrees).
Substituting the given values, we have:
W = (216 N)(12 m) cos(29.5o)
W = 216 N × 12 m × 0.8836
W = 2271.12 J
Therefore, the rope does 2271.12 joules of work on the car to move it 12 m.
To determine the work done by the rope on the car, we can use the following equation:
Work = Force × Distance × cos(θ)
Where:
- Work is the work done (in joules, J)
- Force is the applied force (in newtons, N)
- Distance is the displacement of the car (in meters, m)
- θ is the angle between the applied force and the displacement
Given:
- Mass of the car (m) = 45 kg
- Angle between the rope and the horizontal (θ) = 29.5°
- Tension in the rope (Force, F) = 216 N
- Displacement of the car (Distance, d) = 12 m
First, we need to find the horizontal component of the force applied by the rope. This component is given by:
Force_horizontal = Force × cos(θ)
Substituting the given values:
Force_horizontal = 216 N × cos(29.5°)
Next, we can calculate the work done:
Work = Force_horizontal × Distance × cos(0°)
Since the displacement is along the horizontal direction, the angle between the force and the displacement is 0°.
Substituting the given values:
Work = (216 N × cos(29.5°)) × 12 m × cos(0°)
Finally, we can calculate the work:
Work = (216 N × 0.8763) × 12 m × 1
Work ≈ 2332.0224 J
Therefore, the work done by the rope on the car to move 12 m is approximately 2332.0224 joules.