A car of weight w rests on a slanted ramp attached to a traiter to the car from rolling of the ramp.( the cars braker are off and its transmissions is in neutral). Find the tension in the cable and the force that the ramp exerts on the cars tyres?
A 2kg mass hangs at the end of a spring whose constant is k=400N/M.The mass ia displaced a distance of 12cm and released. What is acceleratin at the instant the displacement is x=+7cm?
To find the tension in the cable and the force exerted by the ramp on the car's tires, we can break the problem down into two components: the gravitational force acting on the car and the normal force exerted by the ramp.
1. Gravitational Force:
The weight of the car is acting vertically downwards. Since the car is on a slanted ramp, this force can be resolved into two components: one parallel to the ramp (mg*sinθ) and the other perpendicular to the ramp (mg*cosθ), where θ is the angle of inclination of the ramp.
2. Tension in the Cable:
The tension in the cable is responsible for balancing the component of the car's weight that is parallel to the ramp (mg*sinθ). This tension prevents the car from rolling down the ramp.
3. Force Exerted by the Ramp on the Car's Tires:
The force exerted by the ramp on the car's tires is the normal force (N) exerted by the ramp in the perpendicular direction. This force is responsible for balancing the component of the car's weight that is perpendicular to the ramp (mg*cosθ).
Now, let's calculate the tension in the cable and the force exerted by the ramp:
Tension in the Cable (T):
T = mg*sinθ
Force Exerted by the Ramp on the Car's Tires (N):
N = mg*cosθ
Note: In both equations, 'm' represents the mass of the car and 'g' represents the acceleration due to gravity (9.8 m/s²).
By substituting the values of 'm', 'g', and the known angle of inclination 'θ' into these equations, you can find the tension in the cable and the force exerted by the ramp on the car's tires.
To find the tension in the cable and the force that the ramp exerts on the car's tires, we first need to understand the forces acting on the car. In this situation, there are two relevant forces: the gravitational force pulling the car downward and the normal force exerted by the ramp on the car.
1. Gravitational force (Weight): The weight of the car (W) acts vertically downward. The magnitude of this force can be calculated using the formula: Weight (W) = mass (m) x acceleration due to gravity (g).
2. Normal force: The normal force exerted by the ramp on the car acts perpendicular to the surface of the ramp. This force balances the gravitational force acting vertically downward and prevents the car from rolling off the ramp.
Since the car is in a state of equilibrium (not accelerating), the sum of the forces in the vertical direction should be zero. Therefore, the normal force exerted by the ramp equals the weight of the car: N = W.
The tension in the cable is equal to the force needed to balance the gravitational force acting on the car. This tension will be pulling the car upwards and preventing it from sliding down the ramp.
Therefore, the tension in the cable equals the weight of the car: T = W.
In summary:
- The tension in the cable is equal to the weight of the car (T = W).
- The force that the ramp exerts on the car's tires is equal to the weight of the car (N = W).
Please note that the above explanation assumes an idealized scenario where there is no friction between the car's tires and the ramp surface. In reality, friction should also be considered, which would affect the force exerted by the ramp on the car.