What force must be exerted to prevent a truck weighing 15 tons from rolling down an inclined plane which makes an angle of 3 degrees with the horizontal.

force= 15tons*sin3deg

wow. 1500 lbs.

To find the force needed to prevent the truck from rolling down the inclined plane, we need to consider the force of gravity acting on the truck and the force of friction opposing the motion. Here are the steps to calculate the force:

1. Determine the weight of the truck: The weight can be calculated by multiplying the mass of the truck by the acceleration due to gravity. The weight of the truck is given as 15 tons. Since 1 ton is equal to 2000 pounds, the weight can be calculated as follows:
Weight = 15 tons x 2000 pounds/ton = 30,000 pounds

2. Determine the component of the weight acting down the inclined plane: The weight can be divided into two components: one perpendicular to the plane (normal force) and one parallel to the plane (force due to gravity). The component of the weight acting parallel to the inclined plane can be calculated by multiplying the weight by the sine of the angle of inclination. In this case, the angle of inclination is given as 3 degrees:
Weight component parallel to the plane = Weight x sin(angle)
Weight component parallel to the plane = 30,000 pounds x sin(3 degrees)

3. Calculate the force of friction: The force of friction opposes the motion and prevents the truck from sliding down the inclined plane. The force of friction can be calculated using the equation:
Force of friction = coefficient of friction x normal force

4. Calculate the normal force: The normal force is the component of the weight acting perpendicular to the plane. It can be calculated by multiplying the weight by the cosine of the angle of inclination.
Normal force = Weight x cos(angle)
Normal force = 30,000 pounds x cos(3 degrees)

5. Substitute the values into the equation for friction: The coefficient of friction is not given in the problem, so we need additional information to calculate it. Depending on the surface and conditions, different coefficients of friction apply. Let's assume a coefficient of friction of 0.4 for now:
Force of friction = 0.4 x Normal force

6. Calculate the force needed to prevent the truck from rolling: The force needed to prevent the truck from rolling is equal to the force of friction.
Force needed = Force of friction

By following these steps, you can find the force that must be exerted to prevent the truck from rolling down the inclined plane.