an empty truck weighs 4000N its engine can produce an accelerationof 1m/sif the truck is loaded with 2000N, find the acceleration the engine can prodeuce?
3/2 the mass, 2/3 the acceleration.
To find the acceleration that the engine can produce when the truck is loaded with 2000N, we need to use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Here's how we can solve the problem step by step:
1. Determine the mass of the loaded truck:
- Recall that weight is a force, so we can convert the weight to mass using the formula: weight = mass × gravitational acceleration (W = mg).
- The empty truck weighs 4000N, so its mass can be calculated as: mass = weight / gravitational acceleration.
- Assuming a gravitational acceleration of 9.8 m/s^2, the mass of the empty truck is: mass = 4000N / 9.8 m/s^2.
2. Calculate the total weight of the loaded truck:
- The loaded truck weighs an additional 2000N. Therefore, the total weight of the loaded truck is: total weight = empty truck weight + weight of the added load.
- Plug in the values to calculate.
3. Find the mass of the loaded truck:
- Again, use the formula: mass = weight / gravitational acceleration.
- Calculate the mass of the loaded truck using the total weight and the same value of gravitational acceleration as before.
4. Calculate the net force acting on the loaded truck:
- The net force acting on the truck is the difference between the force generated by the engine and the resistant force (weight).
- The resistant force can be calculated as the weight of the loaded truck, which is equal to the mass of the loaded truck multiplied by the gravitational acceleration.
- The net force is equal to the mass of the loaded truck multiplied by the acceleration (Fnet = m × a).
5. Determine the acceleration:
- Rearrange the formula Fnet = m × a to solve for acceleration (a = Fnet / m).
- Substitute the values of Fnet and m calculated earlier to find the acceleration.
By following these steps, you should be able to find the acceleration the engine can produce when the truck is loaded with 2000N.