What is the minimum work needed to push a 850 kg car 940 m up along a 9.5 degree incline?
Part A: Ignore Friction
Part B: Assume the effective coefficient of friction retarding the car is 0.20.
a. work= mg*940sin9.5
b. work= work above+mg*mu*distance
what is mu?
The mass times the coefficient of friction
To calculate the minimum work needed to push the car up the incline, we will consider two cases:
Part A: Ignore Friction
When friction is ignored, the only force acting on the car is the component of its weight parallel to the incline. The work done against this force can be calculated using the formula:
Work = force × distance × cos(angle)
The force exerted by the car's weight parallel to the incline is given by:
Force = mass × acceleration due to gravity × sin(angle)
where:
- mass = 850 kg (given)
- acceleration due to gravity = 9.8 m/s^2 (considered constant)
- angle = 9.5 degrees (given)
First, convert the angle from degrees to radians:
Angle in radians = angle in degrees × (π/180)
Next, calculate the force and work:
Force = mass × acceleration due to gravity × sin(angle in radians)
Work = Force × distance × cos(angle in radians)
Substitute the known values into the equations and calculate the work.
Part B: Assume the effective coefficient of friction retarding the car is 0.20
When considering friction, we need to account for the opposing force that the friction exerts. The work done against this force can be calculated using the equation:
Work = (force due to gravity + force due to friction) × distance × cos(angle)
The force due to gravity is the same as in Part A.
The force due to friction is given by:
Force due to friction = coefficient of friction × Force normal
where:
- coefficient of friction = 0.20 (given)
- Force normal = mass × acceleration due to gravity × cos(angle)
Calculate the force due to friction, then substitute both forces into the equation above. Finally, calculate the work.