Two 30kg children in a 20 kg cart are stationary at the top of a hill. They start rolling down the 80m tall hill and they are traveling at 30 km h-1 when they reach the bottom. (The cart had brakes!) How much work was done on the cart by friction during its travel down the hill? (Note: the use of the word on and remember to specify the sign of the work done.)
plese help me to answer this proplem
To find the work done on the cart by friction during its travel down the hill, we need to calculate the change in the cart's potential energy.
The potential energy at the top of the hill can be calculated using the formula:
Potential Energy = mass * acceleration due to gravity * height
The mass of the cart is 20 kg, and the height of the hill is 80 m. The acceleration due to gravity is approximately 9.8 m/s^2.
Potential Energy at the top of the hill = 20 kg * 9.8 m/s^2 * 80 m
Next, let's calculate the kinetic energy of the system at the bottom of the hill. The kinetic energy can be calculated using the formula:
Kinetic Energy = 0.5 * mass * velocity^2
The total mass of the system is the sum of the masses of the cart and the two children, which is 20 kg + 30 kg + 30 kg = 80 kg. The velocity is given as 30 km/h, which needs to be converted to m/s:
Velocity = 30 km/h * (1000 m/1 km) * (1 h/3600 s)
Now we can plug the values into the formula to calculate the kinetic energy:
Kinetic Energy at the bottom of the hill = 0.5 * 80 kg * (30 km/h * (1000 m/1 km) * (1 h/3600 s))^2
The work done by friction can be found by calculating the difference between the potential energy at the top of the hill and the kinetic energy at the bottom of the hill:
Work done by friction = Potential Energy at the top of the hill - Kinetic Energy at the bottom of the hill
Once you have the values, you can calculate the work done by friction.
To calculate the work done on the cart by friction during its travel down the hill, we need to use the equation:
Work = Force x Distance x Cos(θ)
where:
- Work is the amount of work done
- Force is the force exerted (in the direction of motion)
- Distance is the distance traveled
- θ is the angle between the force and the direction of motion
In this case, the force of friction acts against the motion of the cart and children. Since they start rolling downhill from rest, we can assume that the force of friction is the only force acting on the cart, opposing their motion. The angle between the force of friction and the direction of motion is 180 degrees (opposite directions).
First, let's calculate the force of friction. The force of friction can be found using the equation:
Force of friction = Mass x Acceleration
The acceleration can be calculated using the equation:
Acceleration = Change in velocity / Time
In this case, the change in velocity is the final velocity (30 km/h) minus the initial velocity (0 km/h). The time can be calculated using the distance traveled and the final velocity:
Time = Distance / Velocity
Now, let's calculate the force of friction using the mass of the cart and children (80 kg) and the acceleration:
Force of friction = Mass x Acceleration
Next, we need to calculate the distance traveled. The distance is given as 80 meters.
Now that we have the force of friction and the distance traveled, we can calculate the work done by friction:
Work = Force x Distance x Cos(θ)
Since the angle between the force and the direction of motion is 180 degrees, the cosine of 180 degrees is -1. Therefore, the work done by friction will have a negative sign.
Finally, plug in the known values and calculate the work done on the cart by friction.
Please note that in reality, other factors such as air resistance and rolling resistance of the wheels could affect the actual value. Now that you know the steps to calculate it, you can substitute the values and get the exact answer.