A 2000 kg trolley is pulled up a 30 degree hill at 20 km/hr by a winch. How much power is the winch providing?
Steps Please!!
weight down the hill: 2000*9.8*Sin30
power=force*distance/time
chenge velocity (distance/time) to m/s
To calculate the power provided by the winch, we need to use the formula:
Power = Force × Velocity
To find the force, we will use a combination of the weight of the trolley and the force required to move it up the hill. Here are the steps to follow:
1. Find the force due to gravity acting on the trolley:
- Calculate the weight of the trolley using the formula:
Weight = mass × gravitational acceleration
Given: mass = 2000 kg
gravitational acceleration = 9.8 m/s²
- Substitute the values into the formula to find the weight.
2. Find the force required to move the trolley up the hill:
- Decompose the force into two components: one that acts parallel to the incline and one that acts perpendicular to it.
- The force acting perpendicular to the hill is the weight of the trolley.
- The force acting parallel to the incline is calculated using the formula:
Force_parallel = Force_total × sin(θ)
Given: incline angle (θ) = 30 degrees
Substitute the values into the formula to find the force_parallel.
3. Calculate the net force acting on the trolley:
- Add the force required to move the trolley up the hill to the force due to gravity acting on the trolley.
4. Convert the velocity from km/hr to m/s:
- Given: velocity = 20 km/hr
- Convert it to m/s by multiplying by a conversion factor of 1000/3600.
5. Calculate the power:
- Multiply the net force acting on the trolley by the converted velocity.
These steps will allow you to find the power provided by the winch.