A 5.20 package slides 1.57 down a long ramp that is inclined at 13.0 below the horizontal. The coefficient of kinetic friction between the package and the ramp is = 0.305
Calculate the work done on the package by friction.
Calculate the work done on the package by gravity.
Calculate the work done on the package by the normal force.
W(fr) = F(fr) •s=μ•mg•cosα•s=0.305•5.2•9.8•cos13°•1.57 =
W(gr) = m•g•h=m•g•s•sinα=5.2•9.8•1.57•sin13° = …
W(norm) =N•s•cos90°=0
To calculate the work done on the package by friction, we need to use the equation:
Work = Force * Distance * cos(theta)
where:
- Force is the force of friction acting on the package, which is given by the equation:
Force of friction = coefficient of kinetic friction * Normal force
- Distance is the distance over which the package slides down the ramp, which is given as 1.57 m.
- theta is the angle between the direction of motion and the force of friction, which is the angle of the ramp, 13.0 degrees.
So, to calculate the work done by friction, we need to calculate the force of friction first.
The force of friction is given by the equation:
Force of friction = coefficient of kinetic friction * Normal force
To calculate the normal force, we need to consider the forces acting on the package. We have the weight of the package acting vertically downward and the normal force acting perpendicular to the surface of the ramp. Since the package is on an inclined plane, the normal force is not equal to the weight of the package. Instead, the normal force is given by:
Normal force = Weight * cos(theta),
where theta is the angle of the ramp, which is 13.0 degrees.
The weight of the package can be calculated using the equation:
Weight = mass * gravity,
where mass is given as 5.20 kg, and gravity is the acceleration due to gravity and is approximately 9.8 m/s^2.
So, to calculate the work done by friction, we need to follow these steps:
1. Calculate the weight of the package: Weight = mass * gravity.
2. Calculate the normal force: Normal force = Weight * cos(theta).
3. Calculate the force of friction: Force of friction = coefficient of kinetic friction * Normal force.
4. Calculate the work done by friction using the equation: Work = Force * Distance * cos(theta).
To calculate the work done on the package by gravity, we use the equation:
Work = Force * Distance * cos(theta),
where:
- Force is the weight of the package, which is calculated as Weight = mass * gravity.
- Distance is the distance over which the package slides down the ramp, given as 1.57 m.
- theta is the angle between the direction of motion and the weight of the package, which is the angle of the ramp, 13.0 degrees.
So, to calculate the work done on the package by gravity, we follow these steps:
1. Calculate the weight of the package: Weight = mass * gravity.
2. Calculate the work done by gravity using the equation: Work = Force * Distance * cos(theta).
To calculate the work done on the package by the normal force, we use the equation:
Work = Force * Distance * cos(theta),
where:
- Force is the normal force acting on the package.
- Distance is the distance over which the package slides down the ramp, given as 1.57 m.
- theta is the angle between the direction of motion and the normal force, which is the angle of the ramp, 13.0 degrees.
So, to calculate the work done on the package by the normal force, we follow these steps:
1. Calculate the weight of the package: Weight = mass * gravity.
2. Calculate the normal force: Normal force = Weight * cos(theta).
3. Calculate the work done by the normal force using the equation: Work = Force * Distance * cos(theta).