(a) What is the minimum work needed to push a 1150 kg car 240 m up a 17.5° incline with zero friction?
(b) What is the minimum work needed if the effective coefficient of friction is 0.20?
(a) Mass * g * (elevation gain)
(b) Answer (a) + friction work.
(friction work = 240 m * M g cos17.5)
B) answer (a) + (240m*.20*1150kg*9.8*cos17.5)
he forgot the effective coefficient of .20 ...
To find the minimum work needed to push the car up the incline, we need to consider the work done against gravity and the work done against friction (if applicable).
(a) Assuming zero friction, we only need to consider the work done against gravity. The gravitational force acting on the car can be calculated using the formula:
F_gravity = m * g * sin(theta)
Where:
m = mass of the car = 1150 kg
g = acceleration due to gravity = 9.8 m/s^2
theta = angle of the incline = 17.5°
Plugging in the values, we get:
F_gravity = 1150 kg * 9.8 m/s^2 * sin(17.5°)
Next, we calculate the displacement of the car along the incline:
s = displacement along the incline = 240 m
The work done against gravity is given by the formula:
W_gravity = F_gravity * s
Plugging in the respective values, we can calculate the minimum work needed to push the car up the incline.
(b) If the effective coefficient of friction is 0.20, we need to consider the additional work done against friction. The frictional force can be calculated using the formula:
F_friction = coefficient of friction * F_normal
Where:
coefficient of friction = 0.20
F_normal = m * g * cos(theta)
Plugging in the values, we get:
F_normal = 1150 kg * 9.8 m/s^2 * cos(17.5°)
F_friction = 0.20 * F_normal
The net force acting against the motion of the car is the sum of the gravitational force and the frictional force:
F_net = F_gravity + F_friction
Finally, we can calculate the minimum work needed to push the car up the incline, including the work done against friction:
W_total = F_net * s
Plugging in the respective values, we can now calculate the minimum work needed if the effective coefficient of friction is 0.20.