You push a 320 N trunk up a 20.0° inclined plane at a constant velocity by exerting a 213 N force parallel to the plane's surface.

(a) What is the component of the trunk's weight parallel to the plane?

(b) What is the sum of all forces parallel to the plane's surface?

(c) What is the magnitude and direction of the friction force?

upward, perpendicular to the plane

upward along the plane

downward, perpendicular to the plane

downward along the plane

(d) What is the coefficient of friction?

You need to try to grunt through this yourself. I will be happy to critique your thinking.

What force would you have to exert on a 326-N trunk up a 21.0° inclined plane so that it would slide down the plane with a constant velocity? What would be the direction of the force? (The coefficient of friction between the plane and the trunk is 0.329.)

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To solve this problem, you can use the principles of Newton's laws and trigonometry.

(a) To find the component of the trunk's weight parallel to the plane, we need to determine the gravitational force acting on the trunk. We can do this by finding the weight of the trunk, which is given by the formula:

Weight = mass * acceleration due to gravity

From the given information, we know the weight of the trunk is equal to 320 N. The acceleration due to gravity is usually taken as approximately 9.8 m/s^2.

Weight = 320 N

Next, we can determine the component of the weight that is parallel to the inclined plane. We can use trigonometry here. Since the angle of the inclined plane is given as 20.0°, the component of the weight parallel to the plane can be calculated using the formula:

Component = Weight * sin(angle)

Component = 320 N * sin(20.0°)

Now you can use a calculator to find the numerical value of this expression.

(b) The sum of all forces parallel to the plane's surface can be found by adding up all the individual forces acting on the trunk. In this case, we have two forces: the force of you pushing the trunk and the component of the weight parallel to the plane.

Sum of forces = Force pushing + Component of weight

Here, the force pushing is given as 213 N, and we calculated the component of the weight in part (a). Add these two values together to find the sum of forces.

(c) To find the magnitude and direction of the friction force, we need to analyze the forces acting on the trunk. In this case, the friction force acts in the opposite direction to the force you are exerting to push the trunk. It prevents the trunk from sliding down the inclined plane.

Since the trunk is moving at a constant velocity (meaning there is no acceleration), the force you are exerting must be equal in magnitude and opposite in direction to the friction force. Therefore, the magnitude of the friction force is also 213 N.

The direction of the friction force is opposite to the force you are exerting, which is parallel to the plane's surface. So the direction of the friction force is downward, along the plane.

(d) To find the coefficient of friction, you'll need to use the equation:

Coefficient of friction = Friction force / Normal force

However, the problem does not provide the normal force explicitly. The normal force is the force exerted by the inclined plane perpendicular to the plane's surface. In this case, it is equal to the component of the trunk's weight perpendicular to the plane.

The normal force can be calculated using the formula:

Normal force = Weight * cos(angle)

Using the given information, you can calculate the numerical values of the weight and the normal force. Then use these values to calculate the coefficient of friction using the equation mentioned earlier.