What is the minimum work needed to push a 975 kg car 230 m up along a 17.5° incline?
Assume the effective coefficient of friction retarding the car is 0.20?
work needed= change of PE+work done on friction
= m*g*230*sin17.5 + mg*mu*cos17.5*230
check that and think it out.
To find the minimum work needed to push the car up the incline, we need to consider two components: the work done against gravity and the work done against friction.
1. Work against gravity: The force due to gravity is given by the weight of the car, which is equal to the mass multiplied by the acceleration due to gravity (9.8 m/s^2). In this case, the weight (W) of the car is calculated as W = mass * gravity = 975 kg * 9.8 m/s^2.
The vertical component of this weight is given by W_vert = W * sin(θ), where θ is the angle of incline (17.5° in this case). Therefore, the work done against gravity (W_gravity) is W_gravity = W_vert * distance = W * sin(θ) * distance.
2. Work against friction: The frictional force (f) is given by the product of the coefficient of friction (µ) and the normal force (N), which is equal to the weight of the car multiplied by the cosine of the angle of incline (θ). In this case, the normal force (N) is calculated as N = W * cos(θ).
The work done against friction (W_friction) is f * distance = µ * N * distance = µ * W * cos(θ) * distance.
The minimum work needed to push the car up the incline is the sum of the work against gravity and the work against friction:
W_minimum = W_gravity + W_friction.
Now, let's plug in the given values to calculate the minimum work needed:
- Mass of the car (m) = 975 kg
- Angle of incline (θ) = 17.5°
- Distance (d) = 230 m
- Coefficient of friction (µ) = 0.20
Calculations:
1. Weight of the car (W) = mass * gravity = 975 kg * 9.8 m/s^2
2. Vertical component of weight (W_vert) = W * sin(θ)
3. Work against gravity (W_gravity) = W_vert * distance
4. Normal force (N) = W * cos(θ)
5. Work against friction (W_friction) = µ * N * distance
6. Minimum work needed (W_minimum) = W_gravity + W_friction
By following these steps and plugging in the given values into the calculations, you will be able to find the minimum work needed to push the car up the incline.