(a) The free body diagram of the forces acting on the car would include the following forces:

1. The weight of the car (W), acting vertically downwards. This can be calculated as mass (m) times gravity (g), so W = m*g = 1.0 * 10^3 kg * 9.8 m/s^2 = 9.8 * 10^3 N.

2. The normal force (N), acting perpendicular to the inclined plane. This is the force that the surface exerts on the car to support its weight. It can be calculated as N = W * cos(θ) = 9.8 * 10^3 N * cos(8.0°).

3. The frictional force (F), acting parallel to the inclined plane and opposite to the direction of motion. This can be calculated as F = μ * N, where μ is the coefficient of friction (0.23).

4. The tension in the wire (T), acting parallel to the inclined plane and in the direction of motion.

(b) The rate of change of the momentum of the car is zero. This is because the car is moving at a constant speed, which means its velocity is not changing. Since momentum is the product of mass and velocity, if the velocity is not changing, then the momentum is not changing either.

(c) To determine the tension in the wire, we need to consider the forces acting on the car parallel to the inclined plane. Since the car is moving at a constant speed, the net force in this direction is zero. This means that the tension in the wire must balance out the frictional force and the component of the weight acting in this direction. The component of the weight acting in this direction can be calculated as W * sin(θ) = 9.8 * 10^3 N * sin(8.0°). So, the tension in the wire can be calculated as T = F + W * sin(θ).

Question

(a) The free body diagram of the forces acting on the car would include the following forces:

1. The weight of the car (W), acting vertically downwards. This can be calculated as mass (m) times gravity (g), so W = m*g = 1.0 * 10^3 kg * 9.8 m/s^2 = 9.8 * 10^3 N.

2. The normal force (N), acting perpendicular to the inclined plane. This is the force that the surface exerts on the car to support its weight. It can be calculated as N = W * cos(θ) = 9.8 * 10^3 N * cos(8.0°).

3. The frictional force (F), acting parallel to the inclined plane and opposite to the direction of motion. This can be calculated as F = μ * N, where μ is the coefficient of friction (0.23).

4. The tension in the wire (T), acting parallel to the inclined plane and in the direction of motion.

(b) The rate of change of the momentum of the car is zero. This is because the car is moving at a constant speed, which means its velocity is not changing. Since momentum is the product of mass and velocity, if the velocity is not changing, then the momentum is not changing either.

(c) To determine the tension in the wire, we need to consider the forces acting on the car parallel to the inclined plane. Since the car is moving at a constant speed, the net force in this direction is zero. This means that the tension in the wire must balance out the frictional force and the component of the weight acting in this direction. The component of the weight acting in this direction can be calculated as W * sin(θ) = 9.8 * 10^3 N * sin(8.0°). So, the tension in the wire can be calculated as T = F + W * sin(θ).

Knowee AI · Accepted Answer

(a) The free body diagram of the forces acting on the car would include the following forces:

1. The weight of the car (W), acting vertically downwards. This can be calculated as mass (m) times gravity (g), so W = m*g = 1.0 * 10^3 kg * 9.8 m/s^2 = 9.8 * 10^3 N.

2. The normal force (N), acting perpendicular to the inclined plane. This is the force that the surface exerts on the car to support its weight. It can be calculated as N = W * cos(θ) = 9.8 * 10^3 N * cos(8.0°).

3. The frictional force (F), acting parallel to the inclined plane and opposite to the direction of motion. This can be calculated as F = μ * N, where μ is the coefficient of friction (0.23).

4. The tension in the wire (T), acting parallel to the inclined plane and in the direction of motion.

(b) The rate of change of the momentum of the car is zero. This is because the car is moving at a constant speed, which means its velocity is not changing. Since momentum is the product of mass and velocity, if the velocity is not changing, then the momentum is not changing either.

(c) To determine the tension in the wire, we need to consider the forces acting on the car parallel to the inclined plane. Since the car is moving at a constant speed, the net force in this direction is zero. This means that the tension in the wire must balance out the frictional force and the component of the weight acting in this direction. The component of the weight acting in this direction can be calculated as W * sin(θ) = 9.8 * 10^3 N * sin(8.0°). So, the tension in the wire can be calculated as T = F + W * sin(θ).

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